ATA has filed for bankruptcy and is simply discontinuing all operations. There was a time when ATA (then American Trans Air) was the only option other than Aer Lingus for traveling from New York to Ireland. They used to operate charter flights during the summer. I flew on them a few times.
I think it's quite a few years since they flew to Ireland so no travelers to or from here will be affected by the airline's decision to simply close up shop. Anyone with a fully paid ticket is out of luck.