Puzzled why motion sensor set off home alarm while away!
Many things can set off a motion sensor erroneously, though it depends on what sort of motion sensor you're talking about.  There are a number of different types of motion sensors; PIR (passive infrared) is the most common in home security systems.
PIR works by looking for changes in the ambient temperature in areas it's monitoring, the assumption being that if there's a large enough temperature "blob" that's moving across the field being monitored, it's a person.

Assuming you don't have pets, things like a cold draft, or incandescent lights turning on/off, or an insect flying in front of the sensor could all trip the sensor.

Another possibility is an electrical fault of some sort, such that the sensor itself didn't trip, but the alarm system thought the sensor did.  If it's a wireless sensor, you may want to replace the batteries; if it's wired, you should check continuity, and that there's a resistor in place.

I can say that yes, I had a number of false positives from the motion detectors I had; I replaced them with more modern sensors, and haven't had a problem since.  If you really want to cut down on false alarms, you could get a dual technology motion sensor, so that two different ways of detecting movement have to agree before an alarm is generated.