It means that the internal registers are 8 bits wide. That is each operation is performed on an 8 bit value. With a 32 bit processor each operation is performed on 32 bits or four bytes of data.
If an 8 bit Arduino wants to add up two int numbers (16 bits ) then it has to split the operation into two parts. You don’t see this as the compiler does it for you, but it takes longer to perform.
So the wider is the fundamental internal register is the faster operations will be done.