If someone is 'like Mike', they have achieved the peak of physical and mental perfection. Such people will normally be extremely sporty, intelligent and witty, and as such are very rare. The original Mike to whom the phrase refers is long forgotten, but its safe to assume he was great to know, and probably damn fine to look at.
"Damn Timothy, you got hot. You're great looking."
"Why thanks, good chum."
"Yeah, you're really like Mike!"
"Please! You flatter me too much!"