IMAP stands for Internet Message Access Protocol and is a protocol used to access emails via an email client on a remote server.
IMAP is suited for people who want to receive email on more than one device, which nowadays is most people who carry a smartphone. IMAP stores email on remote servers - rather than downloading them to local storage - which is how the e-mails can be viewed on different devices. When your read, download or make any changes to emails on one device, it will synchronise across any other device using the same account. IMAP has the ability to only download the header of an email so it can also be much quicker.