A hot-swappable keyboard is one where the switches can be (un)installed without soldering.
A typical mechanical keyboard switch has two electrical contacts (in the form of little metal legs) to be installed in a PCB. One method is to feed the legs into metal-coated holes in the PCB and solder them in (melt metal into the hole).
A switch about to be inserted into a PCB. Afterwards, the hole will get filled with solder to complete the electrical connection.
Another method is to solder a hotswap socket onto the PCB. Then, the switch pins can be inserted into the special holes of the socket to make a reliable electrical connection without the need for additional solder.
Purple hotswap sockets on a PCB. The “2 @” key already has a switch installed, but not the “1 !” key.
A hotswap socket from above. You can see two pieces of metal in each hole. The switch leg gets sandwiched in between them, always making contact.
Many mechanical keyboards are sold without switches so that you can choose your own (there are a lot to choose from and everyone has their own preferences). That means it must be the customer that installs the switches in the PCB. Soldering has a learning curve, requires a soldering station and supplies, and can be dangerous (soldering iron gets very hot, the fumes are bad to inhale, etc.). Instead, a PCB can be sold with hotswap sockets already installed; then you don’t need any tools (though I highly recommend a switch puller, and a keycap puller if you don’t already have one) and it is easy (but you should still read the tips below). Furthermore, if you want to replace a switch (or all of them), it is much easier and faster in a hotswap keyboard than a soldered one.
First, remove the keycap on the switch you want to remove (and any others in the way).
Next, pinch the top and bottom tabs of the switch using your switch puller.
Now pull upwards. If it does not come out easily, you may not be compressing the tabs enough.
First, make sure the switch is in the correct orientation (line up the switch pins with the socket holes). Ensure the switch pins are not bent! If a pin is bent, straighten it first.
The legs of the switch line up with the socket in the PCB.
Next, put the switch in the plate.
All that is left is to push the switch straight down and it will clip into place. However, if the pins are not completely straight and/or you don’t push the switch perfectly straight, it is possible to damage the PCB (the misaligned switch pin can scratch the PCB or even push the socket off). Depending on your switches and the plate, it may take a lot of force to retract the clips by just pushing the switch, in which case you won’t know whether the legs are aligned until it is too late. For this reason, I recommend pinching the clips with a switch puller (as if you were removing the switch) as you push the switch in. That way, if it is taking too much force, you can stop and check that the pins are straight and correctly aligned.
A switch getting safely installed. The switch puller compresses the switch tabs and the finger gently pushes the switch straight down.