Days to Sync means the period for which emails are stored on your device for offline usage.
We show a period of emails equal to the Days to Sync settings. You can configure the amount of emails shown by using More (o o o) | Global Settings | Sync | Days to sync and select the timeframe you desire.
Once emails are downloaded to your device, offline email access is possible. This helps you be able to access that important email, even when you may not have network service. While your device is offline sync is suspended until network service has been turned back on or restored. Once you scroll down we will download more emails.
Please Note: For Exchange ActiveSync accounts, if you wish to receive emails beyond 1 month, please go to More (o o o) | Various Account Settings | tap the account | Download All Messages when Sync is Unlimited