A macerator toilet or macerating toilet is a toilet fitted with a small motor that runs what is essentially a garbage disposal type blade. When flushed, solid waste is pumped to an enclosed chamber and the waste is blenderized before being pumped into the sewage pipe.
In practice, a macerator is nearly always part of an upflush system, in which the water is not drained from the toilet by gravity, but rather by a pumping system. These systems are fully integrated, so it is common to refer to a macerating toilet as an upflush toilet. Recirculating toilets will also usually have a macerator system, but they are a different kettle of fish.
Macerating toilets are used in boats, RVs, houses with poor water pressure, and toilets that are below the level of the sewage line that they feed into. Macerated waste is easier to pump, easier to drain from RV tanks, and will decompose more quickly in septic systems. However their biggest selling point is that they can be hooked into existing waste lines; whereas a normal toilet requires a thick soil stack drain in the floor, a macerating/upflush toilet can be connected to existing drain lines, even if those lines run along the ceiling. Because they are not gravity fed, they do not need the large toilet tanks for flushing, and many of them are designed to use less water-per-flush than traditional toilets.
In decades past, macerating toilets were known for smelling, clogging easily, and generally being a sign of a second-rate lavatory. (This was particularly true of some older models that used water pressure to run the macerator.) If you flushed anything other than human waste you risked seizing up the toilet, and even depositing too much waste in one sitting could cause toilets to seize up. Even if you were careful with what you flushed, a slow accumulation of hair and etcetera could cause the blades to seize up. While clearing the macerator pump was something you could theoretically do at home, in practice it was generally something you called in a plumber to fix.
Modern systems are much nicer, but as you might expect, there are still some downsides. They use electricity, which would be quite inconvenient during a power outage. They still have a risk of clogging, and still need more attention than a basic toilet plunger in order to get them running again -- which usually means a plumber. They are still a good choice for basements and other areas that do not have easy access to the main waste pipes, and they can be a useful option if you are short on space in a small half bath.