Holmes is interested in the case of the Red-headed League because it is funny, and because it is interesting. He knows that someone is planning something, and he wants to find out what.
I really wouldn't miss your case for the world. It is most refreshingly unusual. But there is, if you will excuse my saying so, something just a little funny about it. (p. 10)
Holmes tells Watson that “the more bizarre a thing is the less mysterious it proves to be” (p. 10), and the case may turn out to be quite simple. As soon as he visits the shop and realizes that the man’s assistant has been digging in the cellar into the bank next door, it turns out to be a simple case indeed. He is able to stop the bank robbery.