It's a "short code" for something - like 32665 is for Facebook (FBOOK) and 46645 is Google (GOOGL). Did you sign up for alerts of some kind? (weather, sports?) Voting on Idol or something like that?
Do you use Mobile IM? Somone sending texts via the internet to you?
Domestic simply means it counts as an out of network text - if you have limited text packages it will count against your allowance. If yo have unlimited texting, it really doesn't mean anything, since you have unlimited.