As a drywall installer or even someone putting up their own drywall, a drywall moisture meter is the only way to "look" behind the wall without damaging the walls. A drywall moisture meter is able to detect moisture behind drywall. Excess moisture behind drywall can lead to structural damage, health issues (mold), pests etc.
If you think leaving your walls to dry on its own will work, it won't. This is an issue that has to be dealt quickly before more leakage happens or mold will start coming into play and it will be very expensive to fix/remove. Buying a moisture meter will allow you not only to detect the excess moisture but also to stop it before any serious damage can occur.