What is the use of base pointer register?

It contains an address, which will be used in calculting the actual address of an operand.

Example (Sytem/360): L R2,12(R3,R4)

meaning:

tempadd := 12 + R3 + R4

R2 := content of memory at tempadd

here R3 is called base registed, R4 is called index register. Or vice versa.