It's basically another name for suicide. All jokes aside though, it's just like a bear hug, except that person sort of jumps on you and squeezes you really hard.
Person One: That hug was really tight, I think I could have died.
Person Two: It was obviously a Russian Hug.
When a man runs up to you, yells "I'm Putin it in!" Gives you a bear hug... But he's got a boner so big and strong it rips through both his and your clothes, and penetrates both your vagina and anus so violently that it creates one big uni-hole but you'll be okay because all Russians cum vodka so it's sterile.
"Girl, that last client jus Russian man hugged me!"
"Well, looks like you're in the fistingbusiness now!"
Boys who enjoy yaoi (a genre in Japan that contains sexual and/or romantic relations between two men); literally translates to "rotten boy"; corresponding female : fujoshi