Well, theres probably a few differing reasons, depending on how the product is designed, most pointedly around what exactly the end user wants, but at it's most basic level, FPGA implementation uses field-programmable gate arrays to reconfigure hardware logic to act exactly like original circuitry. Sort of a hardware replication of original devices that, depending on the maturity of the design, can offer a more accurate and precise execution of native code with near zero-latency as opposed to software emulation inherently having to use a translation layer to emulate the final output. That can lead to a built-in latency deficit, not including additional latency triggers such as modern display protocols, game controllers etc. FPGA devices have to contend with that as well of course, but generally manage it better overall.
Of course, software emulation is advanced enough these days that said latency is not a killer for everyone, and programs use various methods to 'anticipate' latency issues and try to keep cycle accuracy as close as possible. FPGA is still emulation of a sort (it uses hardware to emulate hardware, whereas software uses code to mimic hardware), but I generally prefer the term 'replication' to give core developers their dues, plus FPGA development has, and still does, benefitted from software emulation breakthroughs over the years to overcome issues with certain cores. Current FPGA technology limits the level of device of course, with PS1, Saturn, N64 and such about as far as we can go (3DO will probably never be fully accurate going on dev talk), and that is after years of development in the community - plus, even with newer next generation FPGA devices, you'll still be limited by the fact that this is a niche industry and the complexity of custom chips could be beyond the capabilities of the amateur community. That said, I've had my paws in this area for a long time and never would have thought we would be at the level it is, so who knows ?
Of course, FPGA beyond that is the more consumer focused idea of allowing the use original hardware and software - Analogue etc, effectively creating devices which can act as drop-in replacements for original systems - Mega Drive, SNES, N64, PCE, handhelds etc. That is a very attractive proposition and one which emulation on PC and such doesn't provide. MiSTer can go some of the way with controllers, but software support is a non-runner - apart from recent options like GB on the Heber MultiSystem 2 add-on or CD support with the Superdock for the Superstation One, but they will probably remain outliers. The Polymega, which was originally in development as a FPGA system, ended up as a basic Linux software emulation device, but does allow for rom dumping from original software and peripheral support, but it's actual performance pales in comparison to the various consumer FPGA and MiSTer efforts out there nowadays.
Overall, emulation on PC has its place, and will remain so on more advanced systems, but on everything console and computer up to PS1, FPGA is something that everyone should at least explore. Actually recently gave an older Multisystem 1 to a brother of mine, who up to now had just used a Pi setup for retro and next thing I know, he's gone down the scaler route, turned his old consoles into display props and now just runs the MiSTer for everything.
