The size of the pointer basically depends on the architecture of the system in which it is implemented. For example the size of a pointer in 32 bit machine is 4 bytes (32 bit ) and 8 bytes(64 bit ) in a 64 bit machines. The bit types in a machine are nothing but memory address, that it can have. 32 bit machines can have 2^32address space and 64 bit machines can have upto 2^64 address spaces. So a pointer (variable which points to a memory location) should be able to point to any of the memory address (2^32 for 32 bit and 2^64 for 64 bit) that a machines holds.

Because of this reason we see the size of a pointer to be 4 bytes in 32 bit machine and 8 bytes in a 64 bit machine.