A person, particularly gamer, that gets angry at things that they should have no reason to get angry about. They then proceed to cry and complain about seemingly nothing for too long and this makes them extremely annoying to be around. They can be enraged further by making crying noises or treating them like a child.
"Wow, Harvey just lost a game of Smash and now he's being such a Gay Rage Baby. Waaah! Waaaah! "
Baby rage/baby raging is when someone throws a tantrum or gets mad at something in a video game, sometimes to the point of tears, and acts in manners similar to a small, angry child. The term comes from the twitch emote :babyrage:, featuring an angry baby.
Person 1: "Dude, he's maaddd baby raging in chat right now, are you guys seeing this ?"
Person 2: "Hey, Tom, how would you describe that in a twitch emote ?"
Tom: "I'd say...... baby rage."