A Baby is a very young human being, usually less than about a year and a half old. A baby is also an older human being who acts very immature, see Andrew Schlafly. Babies, being young mammals, are nursed by their mothers until eventually being weaned off toward the age of one year. Babies also generally learn how to talk and walk at around this age. Before that happens, babies communicate by crying or making funny noises (also see Andrew Schlafly) and move around by crawling.
Pro-lifers often claim that embryos and fetuses are also babies, which they use to argue against abortion and birth control. According to them, life and person-hood begins at conception, which has a whole list of legal ramifications. Needless to say, it goes against all common sense to say that a week-old embryo - essentially a microscopic booger - is a human being and a person. Where exactly person-hood begins is not known and the subject of heated debate (it may or may not be the same as when life begins).