When you treat strings as an array, each character contained in the string is actually an element in that array. By determining whether an element exists you can determine whether the string is at least that many characters long. (Obviously the first character is element 0, so $username is actually the eighth character in $username.)
This is slightly faster than strlen() however the reason is somewhat more complicated. Essentially whilst strlen() is a function, isset() is actually a language construct. Calling a function is generally more expensive than using a construct.