I don't understand the differences in Cassette and chainsets.

As an ex smoker, some of the hills around Swansea try and kill me on a regular basis.

I've got 4 options of Cassette:
11-25
11-28
12-25
12-27

And on Chainset I've got:

35/50 and 39/53 with compact or not.

I just honestly have no idea what they mean by that.