There are 2 main email protocols. POP and IMAP.
In a nutshell:
POP email accounts delete the incoming mail from the server as it is downloaded
IMAP accounts leave it on and indeed sync with the server, so whatever is on the server is on your device.
What I do therefore is to set up all my mobile devices with iMap accounts and my PC (Laptop or Desktop) with a POP account, that way as soon as mail is opened on my PC when I get home it is downloaded so I have copies locally and if I then view on my mobile devices the mail is deleted as they sync with the server.
This way your mail can be accessed easily when you are on the move and when you get home and read the mail in order to respond or open/save attachments you dont have to go and delete it from your mobile device. It also keps the mailbox on the server nice and empty = no mailbox full/bounced messages.
If you have just a desktop then POP may be best for you. If you have only mobile devices where you access mail then IMAP may be for you, especially if you want access on more than one device or have other people in the organisation that need to be reading the same mail items.