Bountysource is a place where people who make computer programs can ask for help with problems they need fixed or new things they need made, and other people who are good at programming can help them. Think of it like asking your big brother to help you do your homework, except instead of homework it's computer things.
So let's say someone is having a problem with their program and they don't know how to fix it. They go to Bountysource and they post a message saying "Can someone please fix this problem for me? I'll give you money if you can." Other people who are good at programming see that message and they think "Hey, I can fix that!" So they write some code to fix the problem and they submit it back to the person who asked for help. If the person who asked for help likes the fix, they pay the person who wrote the code the money they promised.
Basically, Bountysource helps people who need computer help find people who are good at computer things and will help them for money.