U-substitution is a must-have tool for any integrating arsenal (tools aren't normally put in arsenals, but that sounds better than toolkit). It is essentially the reverse chain rule. U-substitution is very useful for any integral where an expression is of the form g(f(x))f'(x)(and a few other cases). Over time, you'll be able to do these in your head without necessarily even explicitly substituting.
Why the letter "u"? Well, it could have been anything, but this is the convention. I guess why not the letter "u" :)