"2 Weeks" - This option will only send emails that are younger than 2 weeks to your iPhone, all emails that are older than 2 weeks will not be sent to your iPhone.
"1 Week" - This option will only send emails that are younger than a week to your iPhone, all emails that are older than a week will not be sent to your iPhone.
"3 Days" - This option will only send emails that are younger than 3 days to your iPhone, all emails that are older than 3 days will not be sent to your iPhone.
"1 Day" - This option will only send emails that are younger than a day to your iPhone, all emails that are older than a day will not be sent to your iPhone.
"No Limit" - This option will send all the emails in your inbox and folders to your iPhone.
On the iPhone there is an option called "Mail Days To Sync." This option allows you to save space on your iPhone by telling the server to stop pushing emails to your phone.