"Man-kini" is a term used to describe a pair of short, tight swimming trunks worn by men. It is a combination of the words "Man" and "Bikini". One could argue that because men don't normally wear a top piece with their underwear that "Man-kini" is a misnomer.
The style of bathing suit in question is more commonly refered as a "speedo". "Man-kini" is generally used as a deragotive label, implying the man in question is effeminate.
"Look at the dandy over there in the man-kini."
"I can't stand watching professional male body building; they all wear those slingshot sized man-kinis."