In the "old days", before there were as many manageable varieties of polymer clay available, the old formula of Fimo Classic was so hard to condition that many people had to use a food processor (or "food chopper", as it is sometimes called) to make the clay workable. Though you can still use a food processor to soften clay, it isn't usually necessary, thanks to more malleable formulas of clay.
Apart from conditioning firm or crumbly clay, the food processor can be useful for certain effects-specifically those that require raw or cured clay to be broken into bits or pieces. For instance, most tutorials for faux turquoise recommend using a food processor to chop the clay into nuggets. However, it is possible to come up with alternative methods of producing clay nuggets, if you don't have a food processor at your disposal. For instance, you could try using a (clay-dedicated) cheese grater or just using a craft knife to chop pre-conditioned clay into random chunks.
If you do decide to use a food processor for polymer clay, it is best to devote one bowl and set of blades to polymer clay. Mark them somehow or keep them away from the others. Once they've been used for polymer clay, they shouldn't be used with food again.