The email protocol that allows you to access your mail from multiple devices is IMAP, the Internet Message Access Protocol. It keeps the mailbox and its organization on the mail server, allowing phones, tablets, computers, and webmail sessions to work from the same account.
With IMAP, actions such as reading, deleting, moving, or marking a message can be synchronized across clients. A message read on a phone can therefore appear read on a laptop, and folders created in one client can generally be seen in another. IMAP clients may cache local copies, but the server remains the central source.
This differs from POP3, which traditionally downloads messages to one device and may remove them from the server. SMTP is used primarily to send outgoing mail, not retrieve it, while HTTP is the general protocol behind many web pages and webmail interfaces.
IMAP was designed by Mark Crispin in 1986 as a remote-access mailbox protocol. Standard IMAP commonly uses port 143, while IMAP protected with SSL/TLS, called IMAPS, commonly uses port 993.