I know that they repair everything that concerns engines, but what is the actual day for them. Do they sit in the factories or work in airports?
You ask a very broad question. Jet engine technicians can work in various capacities depending on the job they are hired to do.
In my experience, I worked on the flight-line directly on aircraft removing/installing, performing operational checks, troubleshooting and servicing engines and other systems.
Some technicians work on engines out of the aircraft and in a controlled environment like the factories where engines are made. Others work in repair shops tearing down and rebuilding existing engines.