The Suggestion Box is split between two tabs: Suggestions and SOS.
Suggestions
Paying attention to the suggestions gives you an idea of what your Survivors are happy about, or not so happy about. If a Survivor isn't happy about something, their mood drops and your Public Opinion Rating(POR) will drop. So making sure you take care of the unhappy suggestions is very important.
SOS
Every now and then you will be called upon to make a decision to settle an issue in your town. Depending on the choices you make to resolve the issue, your POR will either rise or fall.
Do your best to keep your POR high to keep your Survivors happy and to get the best daily rewards.