There can be can be many reasons why your cat won't eat.
The first thing I would check is to make sure she isn't sick. Check with your vet to find out how to check your cat's temperature. If your cat has been vomiting or regurgitating its food, a trip to the vet is advised.
If a medical reason has been ruled out, you need to investigate further to find out why your cat doesn't want to eat. Has something happened to upset its routine? Have you had visitors to stay?
Even something as simple as repainting a room could change the way the room smells and be off putting for your cat. If your cat is not eating, with will become lethargic, just like we do. If your cat stops eating and drinking for more than two days, a phone call to the vet is advised.
Is the bowl that contains the cat food small or light? I recently started feeding my cats small portions of tinned food from the tin. Tikki in particular, would push this tin around the room to make sure she got all the food out. Cassie, on the other hand, would delicately eat the gravy, and some of the meat without moving the container. It didn't take me long to start putting the food into a small bowl. Not only was it easier for the cats to feed from, it stopped the very annoying sound of a tin being pushed across the floor for half an hour or so!
Because Tikki is the alpha cat in our house, it is necessary for them to be fed in separate places. It is also necessary for me to 'stand guard' to make sure Tikki doesn't take over and eat Cassie's food.
If the feeding bowl in your house is near where a dog eats, or near a noisy appliance such as a washing machine or dishwasher, this could also be a reason for your cat not eating. On the other hand, some cats are just finicky and will wait until a room is empty before eating.
Cat food that has been left out overnight, or in hot weather, may smell and taste unappetising to your cat. It is also worth noting that cats tend to eat less in warm weather. Some natural cat food can also 'go off' fairly quickly. Raw cat food will also attract more flies and ants than dry cat food. If you store leftovers in the fridge, take them out an hour or so before feeding to let them come back to room temperature. Most cats won't eat food from the fridge (unless it something like chicken or fish).
Some cats don't like changing foods. After introducing some tinned moist cat food to Tikki and Cassie, I bought a different brand of what appeared to be healthy cat food which was on special. Both cats refused to eat it. Perhaps I should have tried mixing it in with the other food to get them used to the new taste. I am lucky in that I live in a small town and was able to change it for the brand they prefer. Since changing from a dry cat food diet to additional moist cat food at night, my cats, especially Tikki, tell me in no uncertain terms when it is tea-time, even first thing in the morning. They still have dry food available for grazing during the day. They will also meow piteously and ask to be fed even after being fed by my daughter. More than once I have been caught out by opening a new can only to be told they've been fed. Who said cats aren't intelligent!
If you are still having trouble getting your cat to eat, it may be necessary to experiment with different types of cat food. These can include grain free, high-fibre, low-protein cat food (check with your vet first) or raw cat foods. As cats are carnivores, animal proteins should constitute 30-40% of their diet. Why not try mixing some special treats such as cooked chicken or commercially available cat treats into their food. As they start eating the treats mixed in with the food, you'll be able to reduce the amount of the treat. I wouldn't go overboard with the cat treats as not only can it become expensive, you don't want your cat to expect this every time it is fed. You could also try giving your cat, a special treat after it has eaten. I'm sure most of us have 'bribed' our children with ice cream or some other treat if they eat their vegetables.
Be aware that older cats or cats with sore gums or teeth can find dry food difficult to chew. For these cats will be necessary to feed them moist cat food.
Just like humans, cats occasionally go off their food so if you find your cat not eating for a day or so, don't be too worried. If it goes longer than this, check with your vet.