G'day Katie,

The groundsheet isn't mesh, it is a solid material.  It won't necessarily keep your tent dry and moisture under the flooring is often due to condensation, and if it rains water can still get between the groundsheet and the tent floor.
Having some dampness of moisture on the tent is just a normal part of camping, and you can offset any issues with this by having an old towel on hand to dry it off as you pack up.

Some campsites have banned solid groundsheets, as it can restrict airflow and smother everything underneath it, so before a trip triple-check with whichever campsite you are heading to as to whether or not you're ok to use this one.

Hope that helps!