As a child, Bamm Bamm is widely recognized as the world's strongest toddler, able to lift up trees one-handed and move them from one part of his front yard to another.
For some reason, he never demonstrates such strength in any of his teenaged incarnations, in particular in the Pebbles and Bamm-Bamm Show. Whether this occurs because he has outgrown his tremendous strength or because he still has it but is far more cautious with it is never revealed. However, in a later continuity in which he married Pebbles Flintstone, he once again demonstrates superstrength, in one case holding back an entire bus with just one arm. This continuity makes no reference to any of the secondary characters from the Pebbles and Bamm-Bamm Show even at the wedding, and Pebbles in this continuity is significantly different from her depiction in the show, so it is probably not the same continuity.
Bamm-Bamm was adopted by Betty and Barney Rubble when they realized they were unable to have children. His biological origins have never been explained.