Compound Inequalities and Domain Restrictions

Alright, I think I wasn’t quite clear on my sticking point:

I know what the latex part means, I meant to refer to the actual \left{${latex}:1,\ 0\right} portion.

I know the \left{ and \right} give L and R braces, but what about the "\\{ }", ":1", and the "\ 0" portions. I’ve just not seen this in the calculator or CL before. Interested in those operators specifically.