After a race last year, my right Achilles was tender and would hurt for the first mile of my runs before the pain went away. Rather than continue to run on it and assume that the pain going away after the first mile was a good thing, I took a couple weeks off to rest it and let it heal itself before getting back to running. I did the same thing when my knee and IT band got tight after a different race.
Our tendency is to run thru those little aches and pains and tight muscles. But, we usually recover and improve better by resting and recovering.
Rest should be a part of your training and like Nancy said, it will help keep small nagging aches and pains from turning into major injuries.
"One machine can do the work of fifty ordinary men. No machine can do the work of one extraordinary man." ~ Elbert Hubbard (1856 - 1915)