Well a very quick rough explanation (and probably minor errors as I'm tired) for noobs.
Computer signals have two possible states: On and Off ie "1" and "0" (Which is why power buttons have this mark)
Binary is a number system made of 2 numbers: "1" and "0" Counting in binary goes like this:
0 1 10 11 100 101 110 111 etc
Trinary has 3 numbers: "0", "1" and "2" Counting in trinary goes like this:
0 1 2 10 11 12 20 21 22 100 etc
anyway back onto binary is base for all computer singals. So for example when you type the letter "O" the binary singal that is sent is: "01001111" which tells the computer to do its magic.
Of course you will end up getting very long lines of binary for certain things, perhaps a security key, thats 128 digits long. This is rather long, so hex is used to make things easier to look at.
Hexadecimal uses 16 "numbers":
0123456789ABCDEF
each "number" represents 4 digits of binary for example:
0 = 0000
1 = 0001
7 = 0111
A = 1010
F = 1111
so using the letter "O" again which is: 01001111 in binary, break it up: 0100 1111, 0100 is 4 in hex, 1111 is F in hex. so "O" in hexadecimal is: 4F.