White hominy is whole white corn kernels soaked and cooked in an alkaline solution (traditionally slaked lime), a process called nixtamalization that softens the kernel and loosens its skin; this is different from grits, which are hominy or plain corn ground into a coarse meal rather than left whole. In Mexico it's called maiz nixtamalizado or nixtamal; 'posole' or 'pozole' is the name of the stew made with hominy, not another name for the hominy itself.
Nixtamalization was developed by pre-Columbian Mesoamerican civilizations and remains central to Mexican and Central American cooking today, particularly in states like Oaxaca, Guerrero, and Michoacán, as well as the American Southwest.
Hominy is the base of pozole (a hearty stew with meat and garnishes) and is used as a filling or in the masa for tamales. In the American South it's often served creamed or fried as a side dish; it also appears in Midwestern soups and casseroles, Peruvian stews, and Caribbean rice-and-bean dishes.
Cooked hominy kernels are soft and slightly chewy, with a nutty, subtly sweet corn flavor, pairing well with garlic, onion, and chili peppers in savory dishes, and occasionally with cinnamon, vanilla, or honey in desserts.