The Bomb Card allows you to target an enemy or neutral territory and kill half of the armies on that territory. You can target any territory that’s adjacent to one of your own territories.
If the number of armies is odd, the remaining armies on the territory will round down. So targeting a territory with 5 armies will leave 2, and targeting a territory with 1 army will leave 0. The Bomb Card does not change the ownership of the territory, even when reducing it to 0. Bombs take place after deployments, but before attacks (and also before abandons/airlifts).
Since it kills half of the armies on a territory, it’s most effective when your opponent builds a single large stack of armies. Therefore, when your opponent has a Bomb Card, you should try to keep your armies into separate smaller stacks when possible to reduce its effectiveness. This can have a big impact on a game’s strategy!