The brim is the top of a container, like the edge of a cup. Also, if a cup is brimming, it’s full.
This word has a couple meanings related to fullness. If a cup is full, it’s filled to the brim. The brim is the top. Containers such as buckets and pitchers have brims too. Also, the bucket is brimming if it's totally full. A brimming container is likely to spill. People can brim too: you can be brimming with enthusiasm or happiness. Like a cup about to spill, you can’t quite contain yourself when you’re brimming with joy.