The button is called the CEOP Report button, (CEOP stands for UK's Child Exploitation and Online Protection Centre), if you click on it, you'll get advice and help about issues such as child abuse (but also viruses and hacking), as well as details on how to inform the police and CEOP.
While all that sounds nice and dandy, there's always the problem of abusing the abuse button. If you make it easy for people to report a site or an individual as a child abuser, simply by clicking a button, some users could become trigger happy and do it even when it's unwarranted.
In any case, Bebo isn't the only social network where child abuse and bullying are common occurences; we can remember several examples on other major social networks such as MySpace and Facebook.