Thanks to Harvey Shore for this explanation of HE bombs:
H.E. (now just written without full stops, as HE) is the official army term for High Explosive.
An HE Shell is an artillery (or tank) shell containing high explosive (as opposed to solid shot, schrapnel, air-burst, HEAT or a wide range of other types of shells for special purposes). HE (high explosive) is the commonest type of explosive filling for a shell or a bomb.
These days, an HE Bomb usually means an aerial bomb (dropped from an aircraft) containing high explosive.
However, in the early 20th Century, the word bomb could be used interchangeably to mean a hand grenade, or a mortar bomb, or an aerial bomb.
Anyway, it was a type of explosive that went off with a big bang, usually blowing up whatever it hit, and scaring the pants off whoever was nearby.