Infancy is the earliest part of a person's life, when they're a baby. It's extremely rare for anyone to remember their own infancy.
An amazing amount of growth and development happens during infancy: babies learn to crawl, laugh, and communicate, among many other things. Infancy is vaguely defined, usually including the time from birth to about one year old. You can also use the word to mean "the very beginning of something," so if your lemonade stand is brand new, it's still in its infancy. The word comes from the Latin infantia, "early childhood," and literally, "inability to speak."