Pearls, I will try to answer your question, though there are people on this thread who are FAR better qualified to do so.
STEP stands for Sixth Term Examination Paper (sixth term of sixth form, that is). It's an examination, or series of examinations, in Maths and is used by Cambridge, who I believe created it, and other high-raking universities to identify the real high-fliers in Maths. As far as I know, Cambridge is the only universiity that absolutely requires it; others, including Warwick, often include it in an alternative offer.
There are three STEP papers, numbered 1, 2 and 3 (with 1 being the 'easiest'). The style of the papers is different from A-levels. I can't telll you much about them as I don't do Maths, but what I have been told by various people is that they really test problem-solving ability, and the ability to choose the right mathematical tools to approach a problem.
The highest grade in a STEP. paper (I think) is a 1. To give you some idea how it can affect your offer, DS has to get 3 x A+ and an A in his a levels (I'm avoiding the '*' because it messes up formatting), PLUS a grade 1 in all three STEP papers. That's for Cambridge. For Warwick, his offer is 3 x A+ OR A+A+A and a Grade 1 in any STEP paper.
I have no real idea how DS is doing with STEP, and I don't think he really does either, except that he finds it hard. As you imagine, I'm feeling a bit  on his behalf.
Hope that helps. I've probably got some of that wrong - happy to be put straight! 