An example of an 8-bit overflow occurs in the binary sum 11111111 + 1 (denary: 255 + 1).
The total is a number bigger than 8 digits, and when this happens the CPU drops the overflow digit because the computer cannot store it anywhere, and the computer thinks 255 + 1 = 0.
Most CPUs use a much bigger word size than 8 bits. Many PCs have a 64-bit CPU. A 64-bit CPU can handle numbers larger than 18 quintillion (18,446,744,073,709,551,615 to be precise).