I finished my maths A-level at the start of this summer (well it was by the Jan exams actually but it's a long story how I finished my course early). At the start of my AS though I applied for maths and further maths, which effectively meant as well as studying further maths on top of maths, I was doing all three applied modules too. The structure of your course seems to be slightly different though.
Regardless, I was fed up of further maths by the second year because you learn lots of theoretical maths in it rather than maths you can apply to real life situations, and I felt it was pretty useless (mainly because of the career path I want to go down), so I dropped it.
In pure, like TheCraig has said, you just extend on the maths you learnt at GCSE level. You get introduced to differentiation and integration really early in the course and then that's probably 70% of the pure maths you do for the next two years, the integrals and the differentials just become more complex. Like at tha start of the first year you just differentiate linear equations or quadratic equations (y=3x, y=2x^3 etc.), but by the end of you pure maths A-level you'll be differentiating logs, trigonometric functions, and lots of other stupidly named phenomena.
In mechanics (my favourite module

) you learn maths which you can apply to a whole lot of real life situations. It mainly focuses on forces acting on objects, and you have to learn these 4 (or it might be five) equations of motion which are all related. It's mainly like "a guy hits a golf ball from X height, and it's travelling Y fast at a trajectory of Z degrees, calculate how far the ball will travel/how long it'll stay in the air/the maximum height the ball will reach before it begins to descend. It sounds complicated but once you do a few they get alright.
I severely disliked stats so I'm not going to say much about that. But you mainly focus on large tables of data and probabilities, and constantly use this graph which I've forgotten the name of (it looks like a big hill lol).
Like I said further maths was useless but you learn some pretty interesting stuff in it, mainly about imaginary numbers (hence the useless-ness).
Sorry about all the writing