C was designed as a very low-level language, so it is close to the hardware. Usually, after a bit of experience, you can predict how the compiler will allocate memory, and even pretty accurately what the machine code will look like.
Your intuition is right: it goes back to ASCII. ASCII is really a simple 1:1 mapping from letters (which make sense in human language) to integer values (that can be worked with by hardware); for every letter there is an unique integer. For example, the 'letter' CTRL-A is represented by the decimal number '1'. (For historical reasons, lots of control characters came first - so CTRL-G, which rand the bell on an old teletype terminal, is ASCII code 7. Upper-case 'A' and the 25 remaining UC letters start at 65, and so on. See http://www.asciitable.com/ for a full list.)
C lets you 'coerce' variables into other types. In other words, the compiler cares about (1) the size, in memory, of the var (see 'pointer arithmetic' in K&R), and (2) what operations you can do on it.
If memory serves me right, you can't do arithmetic on a char. But, if you call it an int, you can. So, to convert all LC letters to UC, you can do something like:
char letter;
....
if(letter-is-upper-case) {
letter = (int) letter - 32;
}
Some (or most) C compilers would complain if you did not reinterpret the var as an int before adding/subtracting.
but, in the end, the type 'char' is just another term for int, really, since ASCII assigns a unique integer for each letter.