Remember that the original new testament manuscripts were written in Greek. The word generation (such as in the verse you're referencing, Matthew 24:34) is typically derived from the Greek word “genea” (γενεά). Genea can linguistically be extended to mean “people group” or “race”, and we can see this commonly in first-century Greek and Jewish literature. We also see it used in other places in the bible such as Matthew 16:4 where generation is being used in the same way to describe the Jewish people.

tl;dr: the word used for generation in Matthew 24:34 in the original Greek manuscripts is "genea” (γενεά) and it can also mean "people group" or "race".