The Executive branch does have the authority to enforce laws, but that authority is not absolute. The President cannot go to the Justice department and say "hey, that guy who committed murder, don't prosecute him, because he promised to pay me a lot of money if I let him off". The President cannot go to the Justice department and say "stop investigating me and my political allies or I'll fire you". That second one is what led to Nixon having to resign.

At least, that's what I think should be the case. The majority in this case disagree. They seem to think that any usage of the powers of President is free from any criminal liability.