I'm also puzzled, and my crystal ball's in the shop getting an oil change (or whatever it is they do after every 10,000 views).
I'm guessing that this comes up when adding a Gmail account -- as a "Gmail / Google Apps" account type -- into AquaMail.
Well then, AquaMail is requesting you to five permission to access the account, or more specifically, email in your account.
It also asks for "basic profile" permission so it can get the account's email id and check that it's what is expected.
This -- permission to access your account's email -- is a mandatory step when adding a Gmail account into AquaMail. Without the permission to access messages, what would be the point?
Now, there is a different way, that is to add the account as "Internet mail" account type.
If you use "Internet mail" type, please be aware that Gmail requires "allow access by less secure apps" to be enabled (on Google's web site):
http://www.aqua-mail.com/forum/index.php?topic=2870.msg21424