instant messaging

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The transmission of an electronic message over a computer network using software that immediately displays the message in a window on the screen of the recipient.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun communication, computing A form of realtime communication where two or more people exchange text messages, usually short, using computers or other devices with communications capabilities.