If both the top and bottom MOSFETs turn on simultaneously, they'll short circuit the supply which will probably be fatal to the MOSFETs unless the current limiting is fast enough to protect them.
schottky diodes, to answer the question which is in the title of this thread, are just normal diodes with low forward voltages, e.g 0.14V, 0.2V only, whereas silicon or germanium ones are around 0.5-0.7V. They're four times costlier too, in my case.
One of the applications is the construction of low-dropout rectifiers (AC to DC converters).
Now that we've beat the diodes to death, ssylee has told us that the motor failed, not the diodes or MOSFETs.
@ssylee,we need more information about the motors. The web page in your pointer shows several different motors, which ones did you receive. Is their voltage rating given? The first thing that I would suspect on a kit like this is that you may have 3V motors. If I recall correctly, your power is 7.2V. If there's any binding in the gears, this would cause a very brief motor lifetime.