Paneer is a fresh acid-set cheese from the Indian subcontinent. Hot milk is curdled with lemon, yogurt, or another acid. There is no rennet and no aging.
It does not melt. That is why cubes can be fried or simmered in a sauce and still hold their shape. Chhana is the softer, moister curd used for Bengali sweets. The word paneer is related to the Persian word for cheese. Buffalo milk is common in the region, as well as cow's milk.
History
Fresh acid cheese in South Asia does not have a single inventor or a single century. The word is connected to Persian panir, and the pressed cheese of north Indian cooking sits in a food culture that also drew on Persian and Central Asian kitchens. Village and home cooks made it because the method needs milk and an acid, not a long-aging cave or a rennet calf.
Two cousins should stay distinct. Paneer is pressed until it is firm enough to cut into cubes for savory dishes. Chhana, also spelled chhena, is the related Bengali curd, softer and moister, used for sweets such as rasgulla and sandesh. This page's alias includes chhana because people search it here. In the kitchen they are not the same step. One is pressed for a curry. The other is worked for a sweet.
How it is made
Milk is brought nearly to a boil and an acid is stirred in: lemon juice, vinegar, or yogurt. The milk separates into curds and whey. The curds are drained in a cloth. For paneer, they are pressed under a weight until the block is firm, then cut. For a softer cheese, they are pressed less or not at all. Salt is not always mixed into the block. The sauce or the salad seasons it later.
No rennet means the protein does not behave like a mozzarella or a cheddar in the pan. The cube softens. It does not become a string or a puddle. That is the entire technical point. A cheese sold as paneer that melts away was not made this way. Home paneer and shop paneer differ mostly in how hard they were pressed and how fresh the milk tasted.
Taste
Plain paneer tastes of fresh milk, slightly sweet, with a mild tang from the acid. It is quiet. A well-pressed cube is springy and a little squeaky. Buffalo-milk paneer is often richer than cow's-milk paneer. Neither should taste sour, bitter, or old.
If the only flavor is the sauce, the cheese is doing its usual job. It takes on tomato, spinach, spice, and smoke from frying. A sour or refrigerated-cardboard taste in the plain cube means it is stale. Paneer is a fresh cheese. It does not improve over a week. Chhana for sweets should taste even cleaner and milkier, because sugar will not hide a sour curd.
In the kitchen
Fry cubes until they are browned on the faces, then simmer them in a sauce, or add unfried cubes near the end so they stay softer. Saag or palak paneer is the spinach dish. Mattar paneer is the pea dish. Paneer tikka is the marinated, grilled or roasted piece. Crumble fresh paneer over a salad if you want a mild milky contrast. Sweets that call for chhana need the softer curd, kneaded until it is smooth.
Do not substitute mozzarella and expect the cube to survive the simmer. Do not substitute halloumi and expect the same mild, unsalted milk taste. Halloumi is salty and minty and wants a hot pan. Paneer wants a sauce or a spice mix. Cottage cheese is the wrong texture. Ricotta is the wrong texture. A firm tofu is the usual stand-in for diners who do not eat dairy, with a different flavor and a similar ability to hold a cube.
Around the world
Paneer is everyday food across north India and in Pakistani and other South Asian kitchens, at home and in restaurants. The diaspora made it a standard menu item in Britain, North America, and anywhere those communities cook. Chhana sweets are more specifically Bengali, and they traveled with Bengali cooks rather than with every curry house.
Supermarkets far from South Asia now sell pressed paneer for weeknight curries. A fresh homemade block is often better than a sour shop block, and the method is short. When a recipe says paneer, it means the pressed savory cheese. When it says chhana or chhena, do not press the curd into a tight brick before you try to make a sweet. The alias brings you to the right family. The dish tells you which member.