The generator takes two random Pokémon and forcibly smushes their usually disparate characteristics together to create an insane new mashup, new name and all. You can also manually select the two monsters that comprise your new creation, but it's much more fun to let the fusion machine work its magic with the 151 original Pokémon in its database. You can get different results based on which Pokémon you plug into the equation, of course, yielding thousands upon thousands of ridiculous results. The first monster you select will provide the head, coloring, and first half of the name for your fusion, while the second monster offers the body and name suffix. That's why you can change the order of the Pokémon in the fusion and get different results; the generator does the rest of the work.
A dizzying amount of work went into ensuring you get, at the very least, a viable split between one Pokémon's head and another's body. Not only did Onsager have to manually separate each Pokémon head from its body and set up custom scripts to shade the resulting Pokémon, but he also had to run code that would properly resize the monster's head on the new body and ensure it looked somewhat plausible.
As Onsager writes, some of the results are "less impressive the others," but that adds to the fun and makes the ones that do work well "much more satisfying."
For example: Try a cross between Meowth and Machoke, named Math. (Interestingly enough, Machop, Machoke, and Machamp all result in differently-colored Meowth fusions all with the same name.) You might also get Weenair, the sinister dragon-like cross between Weezing and Dragonair, two very different pocket monsters that make a surprisingly good combination. There's also Mr. Dactyl, a disturbing cross between Mr. Mime and the prehistoric Pokémon Aerodactyl. And then there's Farter, a mix between the bird-like Farfetch'd and the Ghost-type Haunter. Very chill. Don't mix any of the poison plant evolutions of Oddish, lest you're comfortable with a red, beady-eyed monster, possibly drooling, staring you back in the face.