In the UK and Ireland, premises which sell alcoholic drinks require a licence. 'Public houses' [pubs], bars, etc. have a licence which permits them to sell 'intoxicating liquor' for consumption on the premises, while shops which sell alcohol to take away and consume elsewhere, 'off' the premises, have an 'off-licence'.

An off-license is where you can buy alcohol to take home. In Australia, we call it a bottle-shop, or "bottle-o". I guess "off-license" comes from "off the alcohol-licensed premises"(ie. the usual pub), but a local would explain it better than I could. (I'm basing my assumption on Australian licensing laws, if my logic sounds a little strange.)