League of Legends (LoL) Question: What is this

If you mean your badge awards that you can find both under your name in forum posts or on your profile then it's your awards (you can see what they are if you hover over their respective icons). The burning 1 number indicates that your MF account is 1 year old and the symbol of bronze rank indicates the rank (in this case bronze) you reached during the specific season of that badge, you got the badge when you verified your league account with your MF account.