Basically, there’s a “bump” as the piston switches directions at each end of the stroke, hence twice per revolution.
Vibration is caused by changing force on the crankshaft, which is caused by acceleration of the piston (not the same as speed) or changes in the gas pressure pushing the piston (ignition, valves opening). The vibration peaks happens when the forces peak. If you assume 0 degrees on the crankshaft is the piston at the bottom (and 180 degrees is piston at the top), then maximum speed is at 90 and 270, and maximum acceleration is at 0 and 180, twice per 360 degree revolution.
Edit: fixed a technical error per the following comment from /u/d2factotum
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