While using a good-quality WiFi test app you should be able to get such information as the type of encryption a wireless network is secured with, so you can update it in case the one currently in place is outdated.
The next important piece of information would be the wireless frequency channel the network operates on. A good wireless test app will build you a graph with all the channel usage visually displayed so you can tell which channels are overlapping, which ones are the most occupied, etc.
Another important option that you should expect from a high-quality WiFi test app is heatmaps. A heatmap of your wireless coverage can tell you a lot — you can see where the connection is the strongest and where it is the weakest or non-existent (i.e. dead zones). With such heatmaps you've got all the power to improve the coverage tremendously.