Some Drush commands will take time to complete and generate a long output. In such cases, it is useful to record the output into a logfile. After running a migration script, for example, you would like to thoroughly read the log, so you can check whether each migration step is completed as expected. As for cron runs, you would like to keep a log of them so that when you receive an alert, you can look at the log of the last cron runs to debug it.

Now, before you decide to redirect the output of a command into a log, you should be aware of the nature of input and output streams (http://en.wikipedia.org/wiki/Standard_streams). Each process (Drush executing a command, for example), will have three streams: