Register:

This is a part of Central Processor Unit, so they reside inside the CPU. The information from main memory is brought to CPU and keep the information in register. Due to space and cost constraints, we have got a limited number of registers in a CPU. These are basically faster devices.

Cache Memory:

Cache memory is a storage device placed in between CPU and main memory. These are semiconductor memories. These are basically fast memory device, faster than main memory.

We can not have a big volume of cache memory due to its higher cost and some constraints of the CPU. Due to higher cost we can not replace the whole main memory by faster memory. Generally, the most recently used information is kept in the cache memory. It is brought from the main memory and placed in the cache memory. Now a days, we get CPU with internal cache.

Main Memory:

Like cache memory, main memory is also semiconductor memory. But the main memory is relatively slower memory. We have to first bring the information (whether it is data or program), to main memory. CPU can work with the information available in main memory only.