Limbo's mechanic is the use of what's called the "Rift".
Basically, anything in the Rift cannot hurt anything outside the Rift, and vice versa. Also, warframes in the Rift gain an energy regen. The only stipulation, as well, is that warframe powers can still pass around the Rift. So, a Mesa is still able to damage enemies while in the Rift using their 4th. A Rhino is still able to Stomp, and Ember is still able to World on Fire and run around damaging enemies without being damaged.
Players can't pick up items in the Rift, either, so Survivals and Mobile Defenses are a little more challenging in that way.
The best way to do a Defense is to Cataclysm the pods and jump in and out of the bubble to take down enemies. That, or the really slow but sure way, which is to banish each enemy and take them out one at a time. If you're on a team, Mesa is one of the best frames that synergizes with Limbo. Mobile Defense is similar, but remember that players drop the datamass upon entering the Rift.
The best way to do a Survival...use the Rift as a shield when necessary, pop in to activate Life Support, otherwise, stay out of the Rift and/or Banish difficult enemies and use that 3rd to deal more damage to enemies in the Rift.
In Captures, just Rift Walk and Banish targets. Targets get knocked down, no issues with surrounding enemies cuz you're in the Rift and they're not. You can also capture targets while Rift Walking.
Spy missions, I have yet to see if Rift Walking allows a player to just walk through lasers without tripping alarms, but in Corpus missions, a Rift Walking player can just stroll through Corpus laser doors no problem.
In summary, if you get good with Limbo, you can be hailed by your team as the savior and...well, carry the team (since you can also revive fallen teammates while Rift Walking). You can also be scorned if you're a bad Limbo player.