This is one of those where you may get different answers. Generally, their meaning is similar. The obvious difference is that dislike is more formal, you won't hear it in everyday use as much. Don't like is a negation of like, so it's closer to saying that you don't care for something: you're not interested in it, but you don't have very strong feelings about it. It's just that you can't say that you like it. Dislike is the opposite of like so it's closer to saying that you hate something. Regardless, the context and the tone of what you have to say is going to play a big part here, so it's possible to express a lot of hate with "I don't like" just as easily. But semantically, I think this is a good simple explanation.