AX is the primary accumulator; it is used in input/output and most arithmetic instructions. For example, in multiplication operation, one operand is stored in EAX or AX or AL register according to the size of the operand.
BX is known as the base register, as it could be used in indexed addressing.
CX is known as the count register, as the ECX, CX registers store the loop count in iterative operations.
DX is known as the data register. It is also used in input/output operations. It is also used with AX register along with DX for multiply and divide operations involving large values.