How do you show possession with the word "year" ("year's" vs."years")?

Yes, it is.

You would use years when talking about more than one year with no possessive involvement:

It had been years since I last thought about her.

We have been arguing over the same point for more than twenty years now.

Between the years 1914 and 1918, Newfoundland lost an entire generation of young men to an unspeakable horror that was supposed to be the war to end all wars.

You would use years' when talking about more than one year in a possessive sense:

We agreed to review our agreement in five years' time.

Yes, it is.

Year's means what belongs to the year.
Years means more than one year, but not what belongs to them.
Years' means what belongs to a group of more than one year.