In slang, to "check out" means to no longer have any interest in something and to have stopped caring about it. The Online Slang Dictionary defines it as "to stop caring". It is often linked to the period where you are leaving a job and no longer care about it.
"Check out" has several meanings (Macmillan lists five or six). "To check out" is to end your residence in a hotel, vacating and settling your bill (intransitive verb sense 1 in Merriam-Webster). This sense has also been extended to mean leave other places (Collins). One example is to extend this to mean "to die", where you have effectively ended your stay on the world, checked out from life. Your stay on the planet is over. The sense "to die" has made it into most good dictionaries (sense 2 in M-W as above).
From this, there are uses meaning to have mentally left somewhere, to have given up or be showing no interest. Urban Dictionary gives the example:
The days leading up to your vacation/holiday, when you are no longer interested in work. You show up for work, but you are mentally "checked out."
I need to complete this project, but my vacation starts in two days. I can't seem to concentrate. I've completely checked out.
It also has the more permanent version:
The period of time after you have given notice of resignation from a job before you actually leave. When you don't care about the work you are doing anymore or the general welfare of the business or the staff.
If you check out you are no longer involved mentally: you don't consider yourself to be a part of it. Ivanka Trump was no longer concerned with her father's campaigns, and was moving on to something else. Mentally she had left the building.