A control register is a processor register which changes or controls the general behavior of a CPU or other digital device. Common tasks performed by control registers include interrupt control, switching the addressing mode, paging control, and coprocessor control.
The CR0 register is 32 bits long on the 386 and higher processors. On x64 processors in long mode, it (and the other control registers) is 64 bits long. CR0 has various control flags that modify the basic operation of the processor.