The MCU Wiki has some interesting descriptions of it.
The section where they describe the capabilities really ties back to what Erskine said to Rogers before giving it to him. It took someone of Steve's personality to handle the serum. All of the other attempts with it failed or have flaws. Only Captain America took the serum and didn't become a psychopath or have issues with some aspect of it.
And it was originally a German formula, maybe from when they had the Tesseract (Space Stone), but I'm actually wondering if Thanos' previous failure to "reach his destiny" involved losing the Mind Stone on Earth. And the Germans developed the serum using it.
Super Soldier Serum