They do make mechanical switches that respond to movement - automotive security systems use them. That might be a one step approach - not really an "electronic" solution but something to consider.
With the limited information you provided it's difficult to respond however let me make some assumptions and describe with words, a kind of block diagram of how one system might work.
Sensor might be a microphone, as already suggested. Ideally a very wide frequency response might be helpful. That way you can capture more intelligence from the vibration.
Feed the microphone into a preamplifier and small amplifier. Rectify the output of the amplifier so that you have a DC voltage that will vary somewhat according to the output. Use the DC voltage and an comparator (like an LM339) so that it will toggle when a selected threshold is exceeded. Provide the proper relay driver on the output of the comparator to drive whatever load is desired.
At some point you might provide some filtering - that might hopefully focus on the levels of vibrations that represent what you want to see - leaving out the stuff that you don't want. You could also send the signal to your computer for analysis/triggering. That's a bit more complicated but still within reach.
Hope this helps.