What does Sláinte Gaelach mean?

Slainte (pronounced "SLAWN-cheh") is "Cheers!" "Bottoms Up!", etc. Gaelach means the historic people and language of Ireland. I'm guessing a very close translation would be "To your Irish health!", but that is a guess.

ANOTHER ANSWER;

It looks a lot like the common Irish phrase "Sláinte geal" or "Bright Health" as in a toast. "Sláinte Gaelach" doesn't sound correct. Perhaps it was misheard.