If you dream that you are running for some reason, then such dream could be a suggestion to be not so fast and slow down. If you dream about the race that you are taking with someone else, then such dream represents your desire to be better than the others and reach the victory. If you won this race, you will achieve whatever you like. The running is also the sign of the extra energy you have and trying to export it. If you are the sporty person in reality, then it is very common to dream about any kind of sports.
Read more about dreaming of Race in other dream meanings interpretations.