A long vowel is a vowel sound that is pronounced the same way as the name of the letter itself. For example, the long U sound is pronounced like "yoo," as would be the case in words like "lure" and "tube." By contrast, the short U sound is pronounced more like "uh," as in words like "cub" and "tub."
If you're heading off on a holiday to the United Kingdom, it'll be handy to have certain British slang definitions down pat. It's nice to know what the locals are saying, and it makes it a lot easier to have a conversation without looking (and feeling) like a dolt!