year's - placement of the apostrophe before the s indicates singular noun ownership or possession.
years' - placement of the apostrophe after the s is used in cases where its plural noun showing possession.
years - no apostrophe just an s indicates simply a plural of the subject in question, ie. years, shoes, houses, dogs.
information below taken directly from http://grammar.ccc.commnet.edu/grammar/marks/apostrophe.htm
We use an apostrophe [ ’ ] to create possessive forms, contractions, and some plurals (see below). The apostrophe shows where a letter or letters have been left out of a contracted verb:
I am = I'm
you are = you're
she is = she's
it is = it's
do not = don't
she would = she'd
he would have = he would've
let us = let's
who is = who's
she will = she'll
they had = they'd
Whether or not contractions are appropriate in academic prose is a matter of personal taste and debate. See the section on Tone for a discussion of contractions. Also, ask your instructor before using contractions in a paper that will be graded.
In possessives, the placement of the apostrophe depends on whether the noun that shows possession is singular or plural. Generally, if the noun is singular, the apostrophe goes before the s. The witch's broom. If the noun is plural, the apostrophe goes after the s: The witches' brooms. However, if the word is pluralized without an s, the apostrophe comes before the s: He entered the men's room with an armload of children's clothing. If you create a possessive with a phrase like of the witches, you will use no apostrophe: the brooms of the witches.