Posterity is a noun meaning "future generations." These people of the future could be your children and great-great grandchildren, or any people who are born after you.
If you save something "for posterity," you're hoping that years later people will appreciate it, like a time capsule you bury in the yard. The word comes from the Latin word for "post, after." It's also related to the word posterior, which means "behind, to come after in time." In legal terms, posterity refers to the offspring of a person and it often has to do with inheriting property and who is entitled to do so.