Caffeine is a stimulant, so it does have a short term effect on the brain. It can make you feel more awake and alert (which is why it's usually best to avoid drinking coffee in the evening if you have trouble sleeping, or switch to decaff).

Partly because of this lively effect, and probably also because stopping work and having a hot drink gives you a change of pace and relaxes you, a lot of people find that they think better while having a cup of coffee. This isn't because coffee makes you more creative - it can't put ideas in your head if they weren't already there - but it can help to bring about the conditions that allow your creativity to work.

Also, any ritual activity makes people feel comfortable and lowers anxiety levels, and that again helps you to think more clearly and be in touch with your ideas. It is social too, and the fact that we often chat with friends over a coffee could be another helpful factor.