It turns out that the work that makes the "all this" portion actually fuels the brain. Fitness doesn't make you a meathead at all. In fact, it seems to make you less of one.
In a review of over 100 studies, it was found that: Aerobic exercise improves ability to coordinate multiple things, long-term planning and your ability to stay on task for extended periods." Resistance training, which is much less studied than the aerobic side of things, improves your ability to focus amid distracters.
The same study review found that regular, moderate exercise reverses age-related shrinking of the hippocampus, which is responsible for memory formation.
A Japanes study done on rats may explain why regular exercise helps the brain. It found that exercise depletes the brain's energy stores, but that post-exercise fuel goes straight to the brain and puts the stores at about 60% of the pre-exertion levels for about a day. If the rats continued to exercise regularly, the 60% increase in energy stores became the new normal. This was especially notable in the hippocampus and cortex.
What these two studies tell us is that the brain can be exercised like any other muscle. The strain of a workout will cause the muscle to adapt to be ready for that challenge the next time it's presented. The next time you're working out, remember that you're not just improving your cardiovascular abilities, but also your ability to remember other parts of your life.