The 34th Amendment, if passed, will add the following clause the Article 41 of the Constitution of Ireland.
Marriage may be contracted in accordance with law by two persons without distinction as to their sex.
Currently Article 41 reads as follows:
None of this will be changed by the 34th Amendment, the new text will just be added in at the end.
I will also briefly note that English is the second official language of Ireland, and as such the Irish language version of the Constitution takes priority when there is a difference between the two. An early draft of the proposed Irish text was accidentally phrased in such a way that it would have prohibited opposite sex marriage. Whoops.
There's a lot more relevant information available from the Referendum Commission, an independent body that(duh) provides impartial information about referenda, here, including court decisions about marriage, the rules on marriage, information about civil partnerships, changes proposed by the government if Yes wins, but which aren't actually part of the vote, and laws around children and adoption.
My reputation as a godless, baby-eating, liberal Snuggle Justice Warrior may precede me, but nonetheless I'll state for the record that I'll be voting Yes. Gay people in Ireland are already living together as families. They are already raising children together. Those families deserve the same recognition, treatment and protection as families started by straight couples. I can see no possible legitimate reason why they should receive anything less than equality.
Dig out your Paddy's Day finest and your plastic passports, imagine yourself as Irish, and let us know how you'd vote, ye of NSG.
ETA: Title edited to reflect results.