Hi Beckie,
Christmas is a lovely time to visit Ireland. The pubs and shops and most businesses will be closed on Christmas Day but they'll be open all other times. Some attractions close over that period but most of the big ones will be open e.g. Guinness Storehouse so don't worry, you'll have plenty to do.
Some hotels do Christmas packages where you check in for 2 or 3 nights and have all your meals and some sightseeing included. I was at the Great Southern Hotel in Killarney one year and it was excellent. There will be lots of other hotels around doing that too though.
There are Christmas markets in Galway, Belfast and a great festival in Waterford called Winterval.
Generally, the weather is pretty mild, we haven't had a white Christmas in a long long time. You'll need sweaters and rain jackets and some waterproof shoes but you'll be grand.
It's a lovely time of year for walking and it gets dark early so it's a good excuse to head for the pub, sit by a turf fire and enjoy a warming Irish Coffee and/or a bowl of fresh Seafood Chowder - yum!
Sandra.