What kind of circuit breaker is this?
That is a Square D QO series breaker. The one in question is an AFCI, or arc-fault breaker.

The early incarnations of QO AFCIs had some issues. There were blue, green, purple and I believe another color "test" buttons. How old is this breaker?
An AFCI can trip due to electrical "noise" on the line, motor brushes like in vacuums, etc, any kind of arcing or sparking in the circuit, frayed cords, and more.

Here is a good troubleshooting guide for AFCI breakers right from Square D:
http://static.schneider-electric.us/docs/Circuit%20Protection/Miniature%20Circuit%20Breakers/Arc%20Fault%20Circuit%20Interrupters-AFCI/0760DB0204.pdf

Also, more from Square D: http://www.schneider-electric.us/en/faqs/FA125415/

Here is another very good answer to the same question: https://diy.stackexchange.com/a/74242/19875