Feta is a brined cheese from Greece, and a protected name. The protected cheese is made from sheep's milk, or from sheep's milk with some goat's milk. It is not a cow's-milk cheese.
It is white, salty, and tangy, and it crumbles. It does not melt into a stretch. A cow's-milk cheese sold under a similar name outside the rules is not feta. Keep real feta in its brine so it does not dry.
History
Brined white cheese has been made in the Greek world for a very long time. Milk, salt, and a tub of brine suit a hot climate and a landscape of sheep and goats. The word feta refers to a slice. The modern name settled on this cheese, and Greek cooking built a set of dishes around it.
Other countries, notably Denmark, made a white brined cheese from cow's milk and sold it as feta for years. The cheese was cheap, mild, and everywhere. After a long dispute, the European Union reserved the name feta for the Greek cheese made under the rules. A cow's-milk white cheese from another country needs another name. It can be a pleasant salad cheese. It is not feta.
How it is made
Sheep's milk, sometimes with a portion of goat's milk, is set and the curd is cut, drained, and salted. The blocks then live in brine. The brine keeps them white and salty and stops them drying into a hard rind. There is no long cave aging and no bloomy coat. The cheese can be firm enough to slice or soft enough to crumble, depending on moisture and age in the brine.
Cow's milk changes the flavor and is outside the protected cheese. So does a dry, pre-crumbled cup that has sat without brine until the surfaces are chalky. Barrel-aged or tin-aged cheeses vary. The shopping rule is simpler than the dairy science. Buy sheep's milk, in brine, from the Greek protection, if you want this cheese. Rinse a very salty block if the dish is already salty. Do not soak all the character out of it.
Taste
Feta tastes salty, tangy, and of sheep's milk, with a clean white paste. Goat's milk in the mix can add a sharper edge. It should taste fresh and bright, not bitter and not like old brine that has gone funky in a bad way. A little richness in the paste is a good sign. A completely dry crumble tastes mostly of salt.
Cow's-milk cheeses in this shape are often milder, sweeter, and less sheepy. People who grew up on those cheeses sometimes find true feta stronger and saltier. That difference is the milk and the method. Taste the brine. It should smell like salt and fresh cheese. If it smells rotten or yeasty, the tub has failed.
In the kitchen
Crumble it over a Greek salad with tomato, cucumber, olive, and oregano. Layer it into spinach pie and cheese pie. Bake it with vegetables and olive oil until it softens but does not stretch. Eat a slab with watermelon in summer, which is a classic contrast of salt and sweet water. Use it on cooked greens and on beans.
Do not put it on a pizza and expect mozzarella. It will soften, brown a little, and stay in salty pieces. Do not substitute a dry cotija and expect the brine and the sheep flavor, or a fresh mozzarella and expect the salt. A cow's-milk brined cheese can fill a salad if you are honest that the dish has changed. For a Greek recipe, use the sheep's-milk cheese.
Around the world
Protected feta is Greek. It is everyday food in Greece, not a luxury reserved for guests: salads, pies, and a block on the table. The exported cheese is one of the most cooked-with cheeses in countries that do not make it, because salads and vegetable dishes need a salty white cheese.
The old cow's-milk products still exist under names such as salad cheese or Greek-style cheese. Use those names. Bulgarian sirene and other Balkan brined cheeses are relatives with their own identities, not feta under a translation. When a recipe says feta and then describes a Greek dish, the protected sheep's-milk cheese is the one that makes the dish taste as written.