Maintenance Mode is very useful when you'll be working on a computer that is being monitored. Naturally you don't want to receive alerts or have the monitoring service try to correct things that you are working on. Instead of stopping the monitoring service (and potentially forgetting to start it again), you can indicated the monitored computer is being worked on with Maintenance Mode.
You manually put a server into maintenance mode immediately by right clicking on the computer and choosing Maintenance Period -> Immediate Maintenance: Pause Monitoring.
When you enter Maintenance Mode, you specify how long you expect to be working on the server. No further monitoring of the server will take place until that amount of time has past. Then active monitoring of the server begins again automatically.
In addition to the manual maintenance mode mentioned above, scheduled maintenance is also available. With this feature you can have the monitoring service automatically place a server into maintenance mode based on your schedule. This is often useful when some normal process (a nightly backup process for example) might exceed some of the monitors' normal thresholds.