Infant comes from Latin, and it meant something like: in - not fant-speaking. So, while the words ran togheter it (infant) meant "unable to speak'' (just make a search on Google with the keywords "infant" and "etimology".
You can see here too, if you are short of time.http://www.etymonline.com/index.php?term=infanthttp://en.wikipedia.org/wiki/Infanthttp://en.wikipedia.org/wiki/Infant_%28 ... guation%29
"Infant" means that the child is in his early stages in life. In Brazilian Portuguese many times it can be used interchangeably as in: quando eu era criança/na minha infância. Yet, many times it would be wrong of misleading to do that. To illustrate the point, if you say "a taxa de mortalidade infantil" (infant mortality rate-IMR) you are accurate, sort of. Whereas, if you say "taxa de mortalidade de crianças" it could be children in the ages of twelve, ten, eight, etc. "Saúde/Mortalidade infantil" has to do with tender ages.
It seems like in English they have similar usage, but when talking about childhood in the sense of "infancy" they tend to say "at the tender age of..."etc, not to be misleading.