There really isn't anything more to it than that.
An order is a frequency that changes proportional to the reference speed. The number of the order is how many events occur per cycle.
For example:
A vibration that occurs once per rev would follow this frequency. It is said to be first order. 1st order vibration is typically an out of balance.
A shaft rotating:
600rpm would have a frequency of 10Hz
1200rpm would be 20Hz
2400rpm would be 40Hz
Because 600 revs per minue / 60 seconds = cycles per second
A vibration that occurs two times per rev is 2nd order and would have
600rpm = 600*(2/60) = 20Hz
1200rpm = 1200*(2/60) = 40Hz
2400rpm = 2400*(2/60) = 80Hz
Lets suppose that the shaft we are referencing against is an input chast of a gearbox, with input teeth:
1st gear: 13 teeth
2nd gear: 21 teeth
3rd gear: 33 teeth
And we are detecting a whine of
1000rpm = 216.66Hz
2000rpm = 433.33Hz
4000rpm = 866.66Hz
We can do the same calculation in reverse, to work out the order of the whine, and thus what gear is causing the whine.
216.666/1000*60 = 12.9999 = 13th order
The whine is occurring 13 times per rotation of the shaft, which corresponds to the 1st gear driving teeth.