The 4 in the tinyint should represent the zerofill of the number. You can have a tinyint(50) if you want. All that changes is the left padding of 0's that appear before the number stored. So tinyint(4) with a value of 56 would be 0056. It won't alter the range you are allowed. I believe that the zerofill only works with unsigned numbers, so with a tinyint you can still only have 0 - 255 as a valid range.
After a quick test the number does represent the display range regardless of signed/unsigned. It does not however appear to allow zerofill unless the number is unsigned, so if you were to set tinyint(0) that would result in tinyint(3) since you need three digits to display the range of tinyint. When its signed, it gives me tinyint(4).
So it will automatically dictate the minimum size for you based on the datatype and sign, but anything above and beyond is for zerofill. This would also indicate that it merely represents the number of chars required to display it, rather than to store it (since a tinyint can fit in a single byte).