First of all, credit for coining the terms “soft magic” and “hard magic” goes to Brandon Sanderson. He says a lot more, but essentially, hard magic is magic with rules. Soft magic is magic where the rules aren’t explained if there are any to begin with. Stories with hard magic can use their magic to solve problems. Stories with soft magic cannot.
Secondly, I bring this up because I ran into a wall created by hard magic while writing a story. So I figured I’d list some of the advantages and disadvantages here, as well as some examples, so other people won’t hit the same wall I did.