In the original C programming language (which Java, and therefore Processing inherit many things from), you can specify hexadecimal numbers using 0x as a prefix.  

Forgive my lack of C knowledge if this is a stupid question, but the 0x just means the next 8 digits are a color? It seems like your 0x10 = 16 example makes this seems unlikely. I understand the AARRGGBB part.

No, 0x means the following characters (which may be 0,1,2,3,4,5,6,7,9,a,b,c,d,e,f) represents an integer, expressed in hexadecimal notation.  That number isn't necessary 8 digits long, it could be as short as one digit, and as many as 8 digits (for a 32-bit integer).  

Ah! I get it, thank you. One last question, again just out of curiosity, is there an advantage to 0x(something)? If I wrote 0x0 instead of 0 does it use less space / is it faster?

The advantage is that 0xFFFFCC00 is visually more suitable to express a color (we can easily see each channel) than 4294953984! It is also close of the HTML/CSS notation #FFCC00 that Processing reused as well.
So it is purely for the benefit of the programmer, the numbers are the same after compilation.

I don't want to be rude pushing this too far... but I know that it is less readable than the integer representation. What I meant is it faster for Processing to use say "0x10" instead of "16"? I just thought there might be some kind of advantage to using that kind of representation.

Once it gets to the computer, it's all binary numbers.  It makes no difference.  As phi.lho said, these notations are designed for humans.  Human programmers occasionally choose to use hexadecimal because it makes it easier to pick out the bytes (for example when choosing RGB colors).  Whether you type