I want to execute a command, have the output of that command get gzip\'d on the fly, and also echo/tee out the output of that command.
i.e., something like:
Have a nice cup of tee!
The tee command copies standard input to standard output and also to any files given as arguments. This is useful when you want not only to send some data down a pipe, but also to save a copy
As I'm having a slow afternoon, here's some gloriously illustrative ascii-art...
+-----+ +---+ +-----+
stdin -> |cmd 1| -> stdout -> |tee| -> stdout -> |cmd 2|
+-----+ +---+ +-----+
|
v
file
As greyfade demonstrates in another answer the 'file' need not be a regular file, but could be FIFO letting you pipe that tee'd output into a third command.
+-----+ +---+ +-----+
stdin -> |cmd 1| -> stdout -> |tee| -> stdout -> |cmd 2|
+-----+ +---+ +-----+
|
v
FIFO
|
v
+-----+
|cmd 3|
+-----+