The word itself is literally a Latin word for "offspring."

Not to be nit picky, but there’s more too it then that. The Latin word comes from the ancient Greek word φυτόν, which means plant. While the term can and sometimes was poetically used to refer to offspring, it’s more accurate translation would probably be more botanical in nature, e.g. something along the lines of “fruit” or “produce”— similar to the way we might use the expression “fruit of your loins” to describe offspring.

The more traditional Latin word for “offspring” would be prōlēs, from the Latin preposition prō + the verb oleō, literally “moving toward growth.” This is also where we get the word proletariat, from the Latin prōlētārius, i.e. those whose only contribution to society is their offspring.