Each Badge shows things like in my profile shows I have 500 messages ... But there more different badges some of them shows specific events ,some of them shows how many years ur acc old...
The badges are like some type of recognition for each member of the forum to indicate their support for a certain event or a goal here on the website (like being here for 1/2 years, 500/1000 reaction score, 500 messages, etc). It's nothing special but looks really good on your profile.