There were a couple of theories current when I was a grad student and this was a big area of research. One was that it was useful for solid/liquid reactions as DrCMS suggested. The pressure waves from the ultrasound were supposed to break up the solid particles exposing greater surface area for reaction. There may be some truth to this.
The other reactions that it was supposed to work well on were reactions with rates that were increased by increasing pressure. Again, the theory was that the ultrasound created tiny areas of greatly increased pressure, and the rate of reaction would be increased in those areas. I find this reasoning somewhat questionable.
I tried a few sonication reactions at that time but was never able to see any robust effect, even duplicating literature results. I suspect that a substantial portion of the literature of sonication reactions is bogus. Sonication does increase the rate of dissolution of solids in liquids, probably due to micro-mixing and the disruption of solid particles by pressure waves, which makes it useful for cleaning purposes and for preparing colloids, but I haven't seen much use for it in running chemical reactions.