A bromance is a close but non-sexual relationship between two (or more) men, a form of homosocial

Homosocial

In sociology, homosociality describes same-sex relationships that are not of a romantic or sexual nature, such as friendship, mentorship, or others. The opposite of homosocial is heterosocial, preferring non-sexual relations with the opposite sex...

 intimacy.
Bromance is a portmanteau of the words bro or brother and romance. Editor Dave Carnie

Dave Carnie

Dave Carnie , is a former editor-in-chief of Big Brother Magazine and current writer for numerous publications.-Writing career:...

 coined the term in the skateboard magazine Big Brother

Big Brother (magazine)

Big Brother was a skateboarding magazine founded by Steve Rocco, which was notable for ushering in street skating and the sub-culture of skateboarding....

in the 1990s to refer specifically to the sort of relationships that develop between skaters who spent a great deal of time together.
The contemporary circumstances of bromance separate it from more general homosocial

Homosocial

In sociology, homosociality describes same-sex relationships that are not of a romantic or sexual nature, such as friendship, mentorship, or others. The opposite of homosocial is heterosocial, preferring non-sexual relations with the opposite sex...

 practices and historic romantic friendships.