The phrase "to get the boot" (or "to be booted") means to be kicked out of ANYTHING, and it implies that the person who made the decision is (or should be) angry or upset. It can also be active: "to give the boot" or "to boot". 1. "John's getting the boot from Karen tonight." This means Karen is ending her relationship with John. 2. "I cheated on my wife, so she's giving me the boot." This means the wife wants a divorce OR that she told her husband he must leave the house for a while (or forever). 3. "Joe got booted from the swim team for drinking." This means Joe was removed from the team. Again, the coach was upset. 4. "I got booted in the middle of a chat conversation!" This means the Internet connection (or some program) failed and ended the person's activities. It uses personification (talking about non-living things as if they were human) to "feel" like the computer was angry or mean.

Yes, it's correct. "someone is getting the boot" means he/she is kicked out of something. Out of the job. In a not too pleasant way. (You don't have to understand it literally, but the situation would not be very friendly.) Here is an illustration: http://truthmerchants.com/mag/wp-content/uploads/2009/06/kickbutt_400.jpg