A stealth unit is a unit that does not appear on normal enemy radar, although such units can still be revealed if they move within the line of sight of an enemy unit, or if they move within range of an omni radar.
Some units have stealth that applies only to themselves, while others project a stealth field around them that hides all friendly units within a certain range. The stealth capability consumes energy for most units, so this ability can be turned off. Stealth is very often underestimated. Stealth may seem useless once the enemy has Omni Radar, but this is simply not the case. Omnis have a very small omni range and are very expensive to build (about 10* that of a t2 radar) and also very expensive to run (8* that of a t2 radar, at 2000 power/tick). Deceivers, on the other hand, are very cheap, at only 80 mass and a drain of 25 energy. You cannot target stealthed mobile units unless you have LOS on them and when there is direct fire land units and AA in there its hard to keep a constant view. The cybran have by FAR the best T3 air, because of stealth. A cybran ASF will always win against another ASF (that is not cybran) providing both sides have radar coverage, but not omni. Building a few stealth gens in your base is also a very good idea. The enemy has to scout more, and that requires time and a bit of resources. If you see a large amount of units all circled around nothing you can be 90% sure they are engineers building something nasty, like an experimental or nuke or T3 artillery. with stealth you won't see the engineers. Another reason is when your base is stealthed some people might scout LESS because they won't see changes to your base on the radar so they might not scout as they think there is very little reason to scout as there are apparently no changes.
For a list of all stealth units, see the stealth units category.