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It means that a part of the system can be removed and replaced without disrupting the remainder of the system. The most common situation is a card cage where cards can be removed and inserted. In order for this to occur the power supply should not dip in voltage because of the ins and outs. The signals in the system also have to be not disturbed.
Adding some comment to what flatulent said.
"The hot swappable part of the system can be removed and fitted without disrupting the system". Thing for example in a USB mouse. You can connect/desconnect it when your PC is running and it will work, you don't have to restart your PC like in the old days when you have to fit your mouse in your Laptop and things like that.
I was involved in the design of a cPCI card. These cards were fitted in a chassis (with its backplane, PSU, Fans...), they were hot swappable, most of the specs were in the cPCI Specifications, signals you need (PWR_GOOD#, HEALTHY#...), length of pins in connectors, protocol in extraction/removal.
we use the same terminology in certain IC chips where we can replace an existing chip with a higher version or higher capacity. That means supply voltage and logic voltage levels should match..current rating should match..more ever dedicated pins should stay unchanged..few examples are those with apex and sparten series fpga..same package size but more logic cells ...