In the world of (cheap) printers, "MOSFET" has taken on a meaning of its own.
For a long time, 3D printers have had MOSFETs on board of their motherboards to switch the heated bed. In the past two years or so, we've seen a surge of (mainly) Chinese printers where the on-board MOSFETs (or, more often, the terminal blocks) weren't rated for the high current for the heated bed and would melt down or catch fire.
People then started recommending fixes to these issues, such as using a relay, soldering wires directly to the board (to bypass the terminal blocks) or using an external (better) MOSFET. Eventually, manufacturers caught on and started offering "MOSFET boards" which basically consist of a high-power MOSFET, high-current rated terminal blocks and (often) an optocoupler to isolate the drive signal from the bed power (but this doesn't really do anything; there's no need for this isolation). These boards are meant to be used to switch the high current to the bed directly, without it passing through the main board (and instead, the bed output of the main board is used as a control signal for the MOSFET board).
People often refer to these pre-made "MOSFET boards" simply as "MOSFETs" but there is more to them than just a single transistor.
why it increases the overall operating safety of the printer
Using an external MOSFET board does not increase the safety of the printer at all, unless the main board of the printer is badly designed. There's no reason the MOSFET needs to be external and can't be integrated on the main board. Essentially, any company that is offering a printer "with a MOSFET (board)" is saying that their main board is poorly designed and that they've included a band-aid fix. Or, perhaps, because installing an external MOSFET is such a common "mod" nowadays, they're advertising an external MOSFET because it is what people want to see (even if the main board might have a perfectly capable MOSFET already...).