The background lore of Starcraft is that both the Protoss and Zerg exist as part of an ancient, much more powerful race’s reproduction cycle. These beings, the Xel’naga, seed the galaxy with life. Eventually, over billions of years, two species emerge. One with Purity of Form, which makes them both physically and psychically powerful. These are the Protoss. The other half of the equation is Purity of Essence. This is essentially the ability to evolve and adapt rapidly to any situation. This is the Zerg. Over time as part of a huge Cycle, two races develop these aspects naturally and come together to merge into one. The new race is then powerful enough that the Xel’naga can pass their consciousness onto the new beings and continue their life cycle.
Except something went wrong this time and instead of the process occurring naturally, a rogue Xel’naga tried to force the Cycle through genetic alteration. I’ll leaving out the details because they aren’t important to my point. But the important bit is that the Protoss and Zerg were both genetically engineered to achieve the aspects this rogue Xel’naga wanted.
So the Protoss and the Zerg are both ancient, extremely powerful races genetically engineered to by cosmic gods to be the ideal forms of themselves.
Then we have the Terrans. The Terrans are a bunch of criminals, rebels, and mutants from Earth stuffed aboard some ships and launched off into space as part of an experiment. They crashed near the Protoss and started to thrive in their new corner of their universe. Part of their ‘mutations’ were the development of psychic powers, which are only getting stronger generation by generation.
A henchman of the rogue Xel’naga calls Terran the “product of a failed Cycle.” We know that they were part of the life seeded by the Xel’naga, but unlike the Protoss an Zerg they weren’t genetically tampered with.
How can a bunch of rag tag, lost humans repeatedly win major battles against both the Protoss and the Zerg? It’s by no means constant, and they take a lot of losses in the story, but they do win enough that it’s undeniable they’re competitive.
It’s because the Terrans are not only the products of the same cycle, but they’re the closest to achieving both Purity of Form and Essence.
Essence is about adaptability and evolution. The Terran were dumped in a random corner of the galaxy with nothing the wreckage of their space ships and some supplies, and managed to build a competitive space power out of it. The Zerg could do this, but a huge part of the original Starcraft campaign was the Protoss losing to the Zerg because, except for Tassadar, they were unwilling to adapt and develop new strategies.
Purity of Form isn’t only physical strength, it’s producing psychic powers. Although the Protoss are more powerful psychics than the Terran, the gap is narrowing. Kerrigan and Nova, two of the most powerful Terran psychics are easily competitive against most Protoss. The level of psychic powers among Terran seems to be increasing with time as well. In a few hundred years they could pass the Protoss. We know this isn’t common, because the Zerg spend a huge amount of time and resources specifically attempting to infest and assimilate the Terran, because the Terran are such powerful psychics by galactic standards that they can compete with the Protoss. This means that in all the time the Zerg have been traveling across the galaxy, they’ve never found a race with psychic powers that could match those of the Protoss, except the Terran.
So you have both halves of the Xel’naga formula present in Terran. They have adaptability close to that of the Zerg, and psychic powers close to that of the Protoss. Not as great as either, but strong enough to compete. This makes them the closest living thing to the Xel’naga themselves. Considering that they’re a much younger species than the others, in a few thousand years they could surpass both the Zerg and Protoss.
The proof comes when Ouros, the last Xel’naga transfers his ‘essence’ (not to be confused with Purity of Essence) to Kerrigan. This is the last step of the cycle. In the process she becomes the next generation of Xel’naga. This isn’t just because she’s a powerful psychic, or infested. It’s because she’s Terran. The actual, natural product of the Xel’naga’s cycle.