[ars]

Not at all. IMAP can do a lot of complex operations on the email while leaving it on the server, for example you can have the server search the email, flag it (mark it important, or read, or unread).

POP can download the email, and that's about it.

[fluoridation]

Yeah, because then the client can do whatever it wants with the messages. The operations don't need any further support from the protocol.

[ars]

The idea with IMAP is multiple clients can work with your email - for example your desktop and your phone can both see the same messages and manipulate them, even offline.

Gmail basically is IMAP with a couple extras, and your desktop (via a browser) and your phone (via a dedicated app) can both see the same messages. Only the phone can work offline though, because there is little demand for a dedicated desktop email client, it's always via a browser. But Google could easily make such a thing if they wanted.