Bombers are aerial, ground attack units. Unlike gunships they do not hover near the target and are therefore less vulnerable to AA.
Comparison to other AircraftEdit
A Bomber typically has less health, but is faster than a gunship of the same tech level. Bombers also have an area of effect attack, making them better suited for destroying heavily guarded installations, covering long distances quickly (and thus giving the enemy less time to respond) and dealing with large, individual threats. Gunships can "stick around" in between attacks and do not have to make attack runs. This means that for supporting a ground or sea advance, gunships are often better suited, able to target one target after another. Of course, the area of effect from a bomber can equalise this - meaning that it depends upon the composition of the enemy force as to which is best to use. Remember however that gunships may be targeted by other gunships - a feature not common to bombers.
Torpedo bombers on the other hand perform exactly like bombers with most respects - except that they drop torpedoes, which may only target naval units. Since they can not target hover units, they are not the ideal weapon against everything - making them highly specialised. However, they can target both submarines and amphibious units (even those travelling along the sea floor), as well as coming with sonar - allowing you to find these submarines far easier.
Attack Bombers and Strategic Bombers cannot attack units underwater directly. However, if they attack a ship with submerged units close by, the blast radius from the bombs will damage anything underwater if it's close to the surface. So, for instance if you see a fleet of 7 submarines with a couple of frigates, a few Attack Bombers will take care of the frigates and submarines as well! This can be a big advantage if you're having difficulty with a submersible experimental unit.
However, there's a limit as to how much this works when it comes to units on the ocean floor. Units far from the shore cannot be damage by the bombs damage radius because they are too far underwater. The Seraphim Experimental Bomber is the exception - its blast can and generally will annihilate units within it, regardless of whether or not they are underwater.