"U" is different than the other vowels. If it's the long "u that sounds like " you" the an isn't used. So, a university a union. If the "u" sound is short, where it sounds like "uh" I you use it. An upper bed. An unusual thing. The other vowels always use the an.

In English, "u" is pronounced as "yew" So, because of the consonant sound, you should use "a university" or "a useful thing"

Similarly,some words which DON'T start with a vowel,but where that letter is silent,we would use AN.For example "an hour" because the H is silent.

It's a rule from how the words are pronounced, not how they are spelled. We follow the vowel sound instead of the spelling. I think the other members have already given good examples. :)