There are two general categories of memory: primary and secondary.
Secondary memory consists of the various devices that are able to store data and programs even when the power is off. This includes devices such as hard drives, floppy drives, tape drives, CD drives and DVD drives.
Primary memory is the memory that is intimately associated with the actual working of the computer. This includes memory that holds the start-up routines as well as the current program and data it is working with. There are various forms of primary memory: RAM, ROM and Cache memory.
RAM or Random Access Memory holds the current running program and its associated data.
ROM or Read Only Memory contains certain key routines (small programs). One example, is the set of start-up routines. These take control of the computer when you switch on and ensure that the computer boots-up. Booting-up is the process of starting the computer up so that it is able to load and run computer programs.
Cache memory is very high speed memory that is used by the CPU in executing the individual instructions of the program. It is used to hold items such as instructions that are next in line to be executed and data that is likely to be needed by the CPU.