There's this cat in the neighborhood which doesn't have an owner and I suspect it has never had one since she's very cautious and doesn't get very close.
I left her food sometimes, lately for about a week she is coming around mewing continuously. My first guess was that she is hungry but she doesn't eat or drink and even if she does, that doesn't keep her from mewing again. She even waits for me to leave the house and follows me mewing. Don't get me wrong, that doesn't bother me, I just feel that she wants something and I can't understand her.
What is she asking me for?
If she's not satisfied with food/drink it may be that she is actually seeking nothing more than attention. Adult cats don't meow to each other (in cat-world it's only used to communicate between mothers and kittens) so she's definitely trying to say something to you. As to what, well that's a bit harder to be sure on (sadly there's no cat-translator yet) as a rough meow-vocabulary usually develops between a cat and it's slave-human.
In general terms though you can get a rough idea from the pitch and duration of the meow:
One or two short meows = A standard "greeting" meow, the cat equivilent of "Hi"
Multiple meows, especially if accompanied by a vertical tail = Excited greeting. e.g. “Great to see You!” often there's a subtext of "Have you got any food handy?" Or "Give me some fuss" as well.
Mid-pitch meow = Polite request for something, “I'd like to eat.” or "Play with me" or "Fuss me!"
Longer, more drawn-out mrrroooow = Demand for something, often an escalation of the "Polite Request" e.g. “Open the door. NOW.” or "Feed me puny Human!"
Low-pitch MRRRooooowww = Complaint of a wrong you have done. e.g. “You still haven't field Me!” or "The litter tray is full of poop and I need to go" or "You're ignoring me and it's making me cross!" etc.
High-pitched, realtively loud RRRROWW! = Anger or pain. e.g. "You just stepped on my tail you oaf!"
Hiss = Agression e.g. "Go away!" Or "Don't mess with me or I'll totally claw your face off!" Hissing is used cat-to-cat as is growling as well as to humans.
BRRRUPP! = "Excuse me, coming through!"
PRRRIP! = General happy noise
Chirping/Chittering = Mild frustration e.g. "I can't reach it (the prey/toy)"
Multiple "Yowl!" Sounds = "I'm in heat"
Low-pitched growl = "This food/toy/blanket/whatever is MINE, don't come near!"
From how you describe it I think this is likely a plea for fuss or attention, and as @Mick mentions in his comment you probably want to consider carefully before going ahead as the cat may be looking to bond with you and if you aren't prepared to reciprocate then it may be inadvisable to encourage her.
Vocalisations do vary from cat to cat, some don't even "talk" at all. The nuances of an individual cats "speech" are something that an owner gets used to over time. That said there is substantial overlap across many cats in general terms and the list here is intended as a rough starting point for people like the OP who don't have any history with the cat they are trying to understand, it's not always going to be right but it's better than nothing.
The gist of the question is how to infer what a cat is asking for.
Generally, I make myself available to the cat. Acknowledge their meow, make eye contact, stand in front of them, and wait for the cat to explain what it wants.
That seems to generally work. From experience, cats understand your silent attention as not knowing what to do. Usually, I'll get an indication of what they want in absence of a response from me.
If the cat wants affection, they'll approach you for it.
If they want food, they might start interacting with your hands (where the food comes from, according to them).
If the cat doesn't respond, gently step towards it. The idea is that if it wants you to follow (e.g. my cat brings me to the couch if he wants to sleep on my lap), the cat will start leading you once you move towards it.
It's not impossible that they simply want attention. My cat has a habit of meowing when he's next to me and I'm playing a game; but he stops once I look at him (and might even refuse petting). Sometimes, he just wants to be looked at.
It's also possible that the cat is simply greeting you. Since you don't live together, it's possible that it knows to maintain a friendship with you, even if it doesn't currently need anything.
This is similar to why some cats have a tendency to stay close to you, even if not interacting with you. Our cats always sleep near me, and if I move to a different room, so do they (yet they keep their distance because they want to sleep).
Lastly, if the cat was previously domesticated, it's possible that they're asking to stay with you. Our youngest one was a street cat, who was way too young (4 months) to be out on his own (and from experience, he never got enough time with his mom to begin with).
He approached my girlfriend and meowed to her on the street. Softhearted as she is, she picked him up and walked home with him (with no struggling from him whatsoever). He was incredibly friendly and let us handle him any way we wanted to. It's clear that he had been a pet at one point (knowing about the litterbox etc), so we surmise that he was being especially nice in order to be allowed to stay with us.
In general, if the cat wants something from you, it's up to the cat to explain what it wants. Make it clear that you're listening to its request, and allow for it to figure out how to communicate what it already knows it wants.
If you feel like the message isn't getting across, try doing things and see if the cat engages you.
Neither us nor you know what the cat wants. All you can do is interact with it and get it to reveal its intentions to you.
Feral cats don't meow at people, as a rule. I have cared for some ferals that eventually meowed at me after years of consistent feeding (I have a managed, TNR-ed colony).
Your visiting cat has had contact with people at some point. Its shyness indicates that some of that contact has been negative/abusive/scary, or else the cat has been on its own for so long that its "wild" instincts have resurfaced to help it survive.
The fact that its meowing at you indicates that it trusts you. Long ago memories of having a home may have resurfaced. It may be lonely. It may be desperate for you to adopt it. Other than that, the cat may have a medical condition (pain, dementia, urinary blockage, injury, etc) that needs attention and it is begging you for help.
The long and short of it is, the cat has bonded with you.
It's hard to translate an unfamiliar cat's vocalizations. They tend to develop a "meow-language" with their human companions over time, but this can vary quite a bit between cats. My wife used to have a cat that made a certain sound to say "where is everybody?" after waking up from a long nap, and our current cat makes the exact same sound to say "enough with the petting, you're starting to annoy me now". Obvious vocalizations (growling, etc) aside, it's hard to decipher a cat's vocalizations unless you've been around them for a while.
Instead of trying to understand vocalizations, I've found much better results in learning to speak tail. Tail language seems to be much more uniform across cats. When I encounter an unfamiliar cat, I'll interpret any vocalizations as simply an attempt to get my attention and then focus on body language for the rest.
Congrats! You have managed to start some strong bonding here... Cats in the wild usually do not miew much - it is something mainly happening between mother and kids - but for house cats it also happens between cats and owners (or slaves as the cat probably thinks)... It trusts you and wants attention of some kind, maybe as easy as food or maybe it just wants to tell you it is around - or it feels for some other kind of attention. That it is miewing to you is for me a strong indicator that it is used to live with people.
(Bjarne Braastad at the Norwegian Agricultural University has done a lot of research on cat behaviour, he has written a very good popular science book, but I think it is only available in Norwegian)
If she is meowing to you then she must be used to humans, i.e. not feral. Adult cats don't meow to each other, only to humans after they learn that it gets a response. Unfortunately there is no simple way to determine exactly what she wants - it may just be some fuss and a massage, it may be she wants a home.
Best thing to do is find out if she already has an owner and is just looking for even more cuddles and territory to reign over, or if she is distressed.
Depending on where you live she may have a microchip. Cat charities and vets will have the equipment to read the chip and determine who the owner is.
You could also try a temporary collar to see if she is really ownerless. Some charities can supply them, or you may be able to buy them somewhere. They are made of strong paper. You write your details on them, asking the owner to contact you. If nothing happens in a few days you could consider adopting her or asking a charity to look after her.
She wants you to take her to your home and take care of her and love her. She obviously had an owner who abandoned her, and she is feeling lonely and cold and rejected and miserable, and she wants someone to love her and take care of her and keep her warm and safe.