Overguard is a mechanic that was added to the game only recently (relatively) in update 31.5.
Overguard is 'extra health' but it also applies Ah,
Overguard is available for both Players and Enemies, with a few ways of Warframes generating Overguard and most enemies that have overguard, start out with it.
The main thing to know is that an enemy with Overguard, is mostly immune to Crowd Control with a few exceptions. When it was Introduced, it was similar enough to a number of Warframe abilities that those abilities got translated into Overguard.
Player Overguard
Generally there are a few Warframes capable of generating their own Overguard. Rhino is the earliest example, as his Iron Skin works (now) by applying Overguard. Others like Atlas, Dante, Ember, Frost Kullervo, and Styanax all having abilities that either generate Overguard natively, or with an Augment. A lot of them share this Overguard with the Team, so that's nice - this includes Warframes and Companions but nothing else (like Spectres or Necramechs).
There's also Arch Guns when deployed as Heavy Weapons which give you 2000 overguard for that Tanky feeliThank ng (doesn't last long at higher levels) and the very useful Secondary Fortifier Arcane for Secondary Weapons (naturally) that does 8x more damage against Overguard, and gives you some Overguard back. Very handy, especially for some of the squishier, more CC reliant Warframes.
And here's the important bit - Damage Reduction does NOT apply to Overguard. So abilities, or Adaptation, will not benefit Overguard.
Additionally, overguard has a 'Gate' similar to shields, but it is a flat half second (0.5) but a gate none the less so even one point of Overguard is useful.
Enemy Overguard
A few types of enemies have overguard natively, but in general the most common time you will see it is on the Eximus enemies. Special glowy bastards that are here to ruin your day and your crowd control.
So you gotta kill 'em. But of course, they have Overguard so that can be a little. So what can you do? Besides the obvious sage advice - 'Use More Gun'.
Magnetic Status Effects increase damage to Shields and Overguard
Your Pets like Kubrows and Kavats, can use the Assassin Posture to increase their damage to Overguard by 300%
The Sunika Kubrow in particular has an Ability called Unleashed which allows them damage overguard by 300%
A Sister of Parvos's Hound companion can be fitted with Null Audit which removes 50% of an Eximus's Overguard
And the aforementioned Secondary Fortifier increases your damage to Overguard, but also gives you Overguard in turn.
For me, I often take a secondary with Secondary Fortifier on Warframes like Banshee, Limbo, and Nyx as they're more reliant on their Crowd Control for Survival.
And one final bit - they're immune to most status effects, but while Overguard is active, Cold Status Effects (up to four stacks) will still slow down an Overguarded enemy. Something to consider.