There's 2 parts to this, one is making sure you have armed the bombs. Bombs are not "active" to explode by default, otherwise storage and movement on the ground at your home airfield would be excessively dangerous. Make sure you have toggled your bombs armed before you drop them.
Secondly, you have different fuses you can attach to the bomb. This is done pre-flight (can't change the fuse type in the air!) via the loadout screen. Check the bomb type you intend to carry, and match the fuse option with what you intend to do. I.e. I'm flying a 109E-3b with a SC250. I need to go to the Bombs section of the loadout menu, press Next Bomb until I'm on the SC250, then select fuse type (Dive bomb, Low Level, Hi Alt). If I choose High Alt (which typically is the default) it will show a ">1km" in the fuse selection. This means you have to be higher than 1000m when you release the bomb, to give it time to arm itself (after you've toggled the bombs armed on). Low level bombs have much lower requirements, but generally have much longer fuses. (High Alt explodes on contact, where low level ones might have a 8 second or 14 second delay). Pick the right bomb type for the job, or you risk unexploded ordinance, or still being in the blast radius when the bomb goes off.