The Memory Address Register (MAR) is a CPU

Central processing unit

The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...

 register that either stores the memory address from which data will be fetched to the CPU or the address to which data will be sent and stored.

In other words, MAR holds the memory location of data that needs to be accessed. When reading from memory, data addressed by MAR is fed into the MDR (memory data register

Memory data register

The Memory Data Register is the register of a computer's control unit that contains the data to be stored in the computer storage , or the data after a fetch from the computer storage...

) and then used by the CPU.
When writing to memory, the CPU writes data from MDR to the memory location whose address is stored in MAR.

The Memory Address Register is half of a minimal interface between a microprogram and computer storage

Computer storage

Computer data storage, often called storage or memory, refers to computer components and recording media that retain digital data. Data storage is one of the core functions and fundamental components of computers....

. The other half is a memory data register

Memory data register

The Memory Data Register is the register of a computer's control unit that contains the data to be stored in the computer storage , or the data after a fetch from the computer storage...

.

Far more complex memory interfaces exist, but this is the least that can work.