This mysterious but miraculous device changed the world, but I've never seen what one actually looks like or how it works. Is it permanently installed or easily removed/replaced? EBMM's design is pure genius.
There are all different kinds, but basically a steel or other metal rod that runs the length of the neck & helps to prevent neck warping due to string tension or other factors. Most these days are adjustable--threaded at one end with a nut that you can tighten or loosen (righty tighty, lefty loosey), which then increases or decreases amount of tension of the rod against the anchor rod anchor point & thus causes the neck to bow backward or bow forward when you loosen it.
Most truss rods are not removable & so if it is broken, you pretty much end up having to replace the neck.
That's this idiot's most basic attempt to concisely answer your questions. You could pretty well do a whole book or devote an entire forum to truss rods.