The app is unable to connect to Gmail's servers. This is something outside the app itself.
Can you try rebooting the device? Try mobile data if using WiFi, or the other way around, if you can?
Another idea - in case this is a location specific DNS issue:
...is to press Manual on the initial account setup page, and change server names from "imap.gmail.com" to "imap.googlemail.com" (incoming), and from "smtp.gmail.com" to "smtp.googlemail.com" (outgoing). This should get you different servers, might work better.
Finally - someone was having issues like this before, the app not being able to connect at all, and a full reinstall of AquaMail fixed it. I guess something gets screwed up during the install process sometimes (no, I really can't be any more vague than that -- wish I knew when and how things go bad inside Android....).