The NES games originally ran on a very limited hardware, ROMs could not be larger than 32KB PRG and 8 KB CHR for a great total of 40 KB.
In order to be able to store more data on the cartridge, and thus have larger games with better graphics, Nintendo and other companies included what is commonly known as Memory Mappers in cartridges. First the memory mappers were just a couple of discrete logic chips to get bigger ROM, but then it was so useful that they started to develop custom chips (ASICs) for the sole point of doing memory mappers.
Chips could have more features than purely discrete mappers, such as multiple banks of small size, IRQ generation, and even extra audio channels. Those were able to improve graphics even more than discrete mappers.
Among ASIC-based mappers are :
- The Nintendo MMC series
- The Konami VRC series
- Namco series
- Sunsoft series
- Jaleco, Taito, etc...
Many japanese companies made their own chips for Famicom cartridges. However, in the west only Nintendo was able to make cartridges (there is some exceptions in the US, though). Most games that were localized in the west were then usually "ported" to a MMC mapper (with the notable exeptions of a couple of games from Namco and Sunsoft, that were able to make Nintendo release games using their chip).
The MMC5 is the latest and most powerful of the MMC5 series by Nintendo. It is currently the most powerful mapper released, but was only used in a dozen of games, the majority of which are Koei strategy games. In addition to the features mentioned above, it includes a multiplier (allowing to process some CPU calculations faster), extra VRAM, and an extra graphic mode allowing to bypass a palette limitation of NES graphics, as well as using 16384 different tiles without software intervention (as opposed to normal 256). (Basically the "name table", or screen map, becomes 14-bit indexes instead of 8-bit).
A "MMC5 conversion" is basically hacking a game to replace it's mapper by Nintendo MMC5. It is a completely useless process if you don't hack something else to make usage of the MMC5 itself. Usage of the multiplier or extra graphics mode is not possible to use because the original game didn't account for them. So it completely useless unless you do some very extensive
hacking that makes usage of the MMC5 somewhere (by very extensive I'd mean : Completely new graphics)
Some people just think that their favourite game using MMC5 sounds "powerful" or "cool" or something in the like....
EDIT : Here
is a quick look on the features of the MMC5