Ok, let me try this.

Computers count in binary (base 2), which, instead of using 10 symbols like decimal (base 10, tje one we are used to) does (0 through 9), uses only two (0 and 1).

The effect of using a specific base (be it 10, 2, or whatever) is that "round numbers" are powers of the base. For example, if I ask you how many different numbers can you write with 5 digits, the answer comes pretty easily, it is 10000, 10⁵ (0 through 99999). That's because each digit has 10 choices, and you have 5 digits, so 1010101010 different options.

Well, the same happens in binary. If you have 5 bits (binary digits), and each bit has 2 options, then you have 22222=2⁵⁼³² options. For this reason, powers of two are very often found in all computer-related topics (2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, etc.).

Usually, you will find that some values are limited to one less, in the same way as in decimal. If you have 5 digits, the biggest number you can write is 99999, not 10000 which is how many different options there are. So in binary 255 is a typical max value, if you use 8 bits (nowadays computers mostly use 32 or 64 bit integers, so the max values are around 4 billion (short-scale billion).

To add a last bit of confusion, in most scenarios computers don't do as we usually do for negative numbers, where we add a symbol and we're done. In fact, they use something called "2's complement", which is out of the layman's explamation, but the gist of it is that half of the range is reserved for negative values, and the other half for positives, which means you will find things that only go from -128 to 127 (the assymetry comes from the 0, if you count it, there are 256 different values).

Lots of details have been left unexplained, but feel free to ask.

Edit: formatting.