Qui-what? According to Wikipedia, Quiesce is used to describe pausing or altering the state of running processes on a computer particularly those that might modify information stored on disk during a backup in order to guarantee a consistent and usable backup.
In SharePoint, quiesce allows you to reduce the number of users that are connected and takes long running apps slowly offline (think Forms Services here). It prevents the loss of data – and is good practice when performing server maintenance. It has 3 statuses: Normal, Quiescing, and Quiesced. Quiescing is when the connections are being reduced, and when the status is Quiesced new connections aren’t started.
In Central Administration, under Operations you’ll find the Quiecse feature for SharePoint.
Enter the time-period that your farm should be quiescing, and click on the Start button. It will start the process, and will be fully quiesced at the end of the time span.
When your farm is done with its maintenance period, you can un-quiesce the farm by clicking on the Reset Farm button.