In the audio realm, "filter order" is synonymous with "filter pole". Both terms are interchangeable with one another.

Alternative name​
1st1-pole6 decibels per octave filter
2nd2-pole12 decibels per octave filter
3rd3-pole18 decibels per octave filter
4th4-pole24 decibels per octave filter

A 1st order filter has a roll-off rate of 6 dB/octave. This means it attenuates frequencies by 6 dB starting from its cut-off point. For example, if the cut-off point for a low-pass filter is set at 100 Hz. Frequencies below 100 Hz will be reduced in amplitude gradually with a roll-off rate of 6 decibels for every octave. The same is true for the rest of the filter orders.

However, the higher the filter pole the more aggressive the amount of attenuation and phase shift. As a result, you may not want to use steep filters or brickwall filters, particularly in audio mastering. A gentle first-order or a second-order filter is more than enough. Lastly, there is also nothing wrong with not using one because people tend to aggressively high-pass filter every single sound these days. In a way that's a good thing but it can make a mix sound thin if it has been done without caution.