One byte can be used to encode any integer between 'O' and inclusive
One byte can be used to encode any integer between 'O' and inclusive is a 255
Sometimes you hear a group of four bits called a nibble. The largest number you can represent with 8 bits is 11111111, or 255 in decimal notation. Since 00000000 is the smallest, you can represent 256 things with a byte. (Remember, a bite is just a pattern.
A bit is a binary digit. So a byte can hold 2 (binary) ^ 8 numbers ranging from 0 to 2^8-1 = 255. It's the same as asking why a 3 digit decimal number can represent values 0 through 999, which is answered in the same manner (10^3 - 1). Originally bytes weren't always 8 bits though.