The symbol K has a pretty straight forward history. We got it from the Romans, who used it—sometimes—in their Latin language. They got it from the Greeks, where in its lowercase form it was κ and its uppercase is indistinguishable from ours. It can also be seen in Hebrew as כ. Slightly different, but K was often written backwards and if you take of the vertical slash it resembles kaph somewhat. Both kaph and kappa come from the proto-Sinaitic kappu. If you look at the alphabet.gif, you can see the origins of K in there.
From the origins of our Latin based writing system, K was in competition with C. The Romans preferred to use the latter and as you know, pretty much anything the Romans did stuck. You might not remember this from when I went over C’s history (over a year ago! Wow!), but the influence of the Irish language involved consonants with different pronunciations based on what vowel follows. We kind of kept that with C. After e and i (and y), it’s almost always “suh”; after a, o and u, it’s “k”. The main reason K is used is to put the “kuh” sound in front of e and i, as in the words keep and kit.
So K is our backup C. It handles the words C can’t because it doesn’t go soft in front of e and i.