WARNING: None of this has been confirmed by DE. This blog post will contain references to Warframe codex entries, my ideas and speculation on Umbra, and will contain spoilers from the Second Dream. YOU HAVE BEEN WARNED!
We don't know much about Umbra, except that they are supposedly darker variants of the Warframes, the Shadow Stalker uses one, and that Excalibur Umbra will be coming to the Global build first. Recently, I reread the Excalibur Prime codex entry and found a couple interesting lines that could be related to Umbra. This quote has interested from long before the Second Dream came: "We took the twisted few that had returned from that place. We built a frame around them." I believe that this is referencing Umbra in that they were the actual original Warframes. The ones where the Orokin built literal metal frames around them and sent them into battle. "But the Tenno are normal looking teenagers, they don't look anything like the Warframes." you say. But that is where the preceding line comes into play. "We took the twisted few that had returned from that place." What comes to mind when you hear the word "twisted"(I know that twisted could mean any number of things, this is my opinion)? Simply look at Chroma or Saryn or any number of frames. They definitely look twisted. So how do our Tenno fit into all of this?
Here's my thought on the matter. The Orokin had begun experimenting with Void energy and some of them got infected with the Void energy transforming them into monstorous creatures with unexplainable powers. Of course, the Orokin were obsessed with perfection and built a suit-able body around them (sorry, bad pun). The Orokin Executors decide that they are going to colonize the Tau System.To protect future incidents like this one, the Orokin design a Void-resistent suit to protect them from transforming the way the umbra's did. This suit is the one the Tenno wore abord the Zariman. However, as referenced by our powers the suit did not completely protect us from the Void. Transforming us into the Tenno we know today.
Now the Old War has started. Once again the Orokin, try to make a perfect world and put them into cryosleep, to prevent them from harming the public. This is referenced in the Rhino Prime codex where Davis and the narrator are confronted by what I believe is not actually Rhino Prime, but actually Rhino Umbra. The two (presumably Orokin) find themselves in what they thought to be a morgue but actually contains the sleeping children of the Zariman. From his codex we also know that the Orokin have begun experimenting on the original Void-afflicted. In the scene, the creature is going on a rampage and stops when Davis faces it. Why it stops; I have no idea. But I presume the promotions that Davis mentions in the last sentence from the codex are him contemplating the idea of using the Tenno for war. But to do so more experimentation will follow to fuel the Tenno's hatred for the Orokin
As the Orokin start to lose the war, they start sending children to the Void. Margulis develops Transference and the Orokin start to turn the tide of the war. The Warframes that the Tenno use at this time are the Primed variants. Retired from the attempt to weaponize them, the Umbra's are placed in the rank of low Guardians. A title which was held by the Stalker. While the Umbras were experimented on, they remained feudal to the Orokin. After the defeat of the Sentients, the Orokin get wiped out by the Tenno while the Umbra's watch. This starts the Stalker's quest for revenge for his former masters. And the rest is history
TL;DR: The Umbra's are Orokin warped by the void in frames that were the inspiration for our Warframes. They are also the first Warframes to be developed.
I hope you enjoyed my theory on what the Umbra's are plus some of their history. If I missed anything or you have something to add, please put your input in the comments.
Excalibur Prime Codex: Excalibur Prime
Shadow Stalker Codex: Shadow Stalker
Ember Prime Codex: Ember Prime
Rhino Prime Codex: Rhino Prime