An instant message, or IM, is a small window that pops up when you and a ' buddy' are on-line at the same time and one of you sends a message to the other. This allows for real-time conversations to take place on-line. It's similar to a chat room, but just between two people.
Each person must have the IM software installed, allow others to IM you (you can block messages), and be on the other person's list of people they're interested in.
If you are all set up and the IM software running (it runs in the background), when a person on your list logs on to the Internet, message will pop up (or a sound depending on how you have things configured) to let you know that a 'buddy' is on-line. You can then send them an Instant Message and they have the choice to answer or ignore.
The Instant Messaging software is free from a number of sources such as AOL, Yahoo, ICQ, OnLineCall (this one supports video and voice as well). There are others