While the term is not found in the OED it has an interesting etymology.

From (greek): desmos meaning "captive" and dromos meaning "in the shape of a racecourse". Engineering practice generally prefers the use of positive actuation to springs, however the practical challenges of producing a desmo valve train have eluded most engine builders.

The primary effect of using positive actuation in place of spring actuation is the obvious elimination of valve float. Valve float occurs where the force available from a valve spring limits the speed with which a valve can close and hence the maximum RPM of the engine.

What is less obvious are the secondary effects.

Valve springs typically weigh as much as the valves which they actuate, thus the total mass which needs to be moved by the actuation mechanisms (belts, bearings, shafts) also need to be larger in order to avoid fatigue failures. The combined weight of the mechanism and the energy needed to overcome the spring forces and added frictional forces means that a larger fraction of the engine's available power output is being used for valve actuation. (High frame-rate film imaging of running engine-valves also illuminate how the valve spring's resonant frequencies can rob the valve of return-force.)

Finally in addition to potentially allowing higher engine RPM, a desmo valve train allows the valve cam profile to actuate the valve faster and keep the valve at full-open longer. This translates directly to higher available torque across the entire operating range, and is probably more important in the overall design than peak RPM alone.*

Ducati produces a variety of motorcycles using both 2 and 4 valves per cylinder. The primary downside of these machines is the more frequent maintenance interval. This can be addressed with an improved valve collet design from the aftermarket vendor, http://www.mbpducati.com/

* Generally, engineering practice prefers the use of positive actuation over spring-actuation wherever possible, this is an instance where the benefits are synergistic