They can be talked to and asked about their parents, who are "around here somewhere." They will ask people carrying a weapon if they intend to kill someone.
Killing any one of these grants the title of Childkiller.
These children have sprites for throwing, which means they are also capable of throwing grenades.
In the Fallout 1 versions of the game released outside of the U.S. (including the GOG release), the children were removed to avoid controversy about child killing. However, the children can still be killed with explosives as only their sprites were removed.
Little Bobby - Orphan child in the Den Residential.