Drive controls the input gain to the non-linear algorithm, and slope, clip and edge all control its profile. In addition asym makes it different for positive and negative signal excursions to create even as well as odd harmonics. The actual transfer function can be seen in the graph. The lo cut filter is to remove 'beating' caused by intermodulation, and the hi cut to reduce the level of added harmonics to the desired level. The mix controls how much of the processed non-linear signal is present in the output compared to the unprocessed signal.
In this case, the shape can be seen, the mix is 100% of the processed signal, and the hi and lo filters are set to 436 and 3442Hz respectively.