This could be due to a few reasons, but it generally falls under at least one of the below reasons:
Humidity and Moisture: Basements are prone to high humidity, which can be tested with a hygrometer. If the humidity levels are high, this leads to mold, mildew, and rot; all of which give off odd odors.
Water Leaks: If water has a way in, it will get in. Without a system to address this, the water will product water mold, and musty odors. Even if you can't see standing water, a small crack in a corner can house a water issue.
Efflorescence: This occurs when salts are brought through the foundation walls, carried by water, which then evaporates, leaving behind a white mineral deposit. While this in itself is not harmful to your health, it is a sign that the space is to damp and that can cause the odd odor.
Rotting Wood: If water has made its way into the wooden pieces of your home, or wooden items within the basement, it can cause rot, emitting an odor.