What is the relation between ROM Manager, ClockworkMod and Nandroid? Which one(s) do I need?

So I understand the first thing I need to do with my phone, after rooting, is to back everything up. But I was confused about 3 of the apparently popular tools used for this. For example, is Nandroid an application I run on a computer connected to the Android device, or on the device itself? I understand ClockworkMod is a "custom recovery". What does that mean? Why do I need it? What does it mean to "flash" it? Asides from browsing and installing new ROMs, how does ROM manager interact with the other two? Does it include them both, so I just need to download it from the market and be done with it? I will appreciate any answer that can sort out the differences, with emphasis on what I, as an end-user, actually need to do, and whether there is any risk on those actions.