In terms of audio production “dynamic” is a range in level between the quietest and loudest peaks. If within a recording our quietest moment is -20dBFS and our loudest moment is -3dBFS Then we have a dynamic range of 17dBFS. While in a DAW you will often find the full dynamic range as something like -60dB to 0dB, This is the headroom for the dynamics of the audio.
So dynamic processing is any processing that results in a change of the recorded dynamic range.
These processes can include a range of different processing tools that achieve differing results, effects and solutions. Compression is in fact a reduction of dynamic range based upon a threshold and ratio., it’s often thought that compressors make things louder when in fact they make loud things quieter.
Multi-band compression is reduction of dynamic range based on ratio, threshold and frequency range.
Limiting is compression at extreme values, generally the ratio is fixed and a threshold is the key control for these tool types. A compressor with a ratio of 20:1 is considered limiting
A noise gate reduces the level of quiet sounds while leaving louder sounds untouched based upon a threshold and ADSR style controls
Expansion is the opposite of compression and can be used to increase the dynamic range of a piece of audio, this can be particularly useful when something has been recorded with a lower than adequate input level. If the bit depth of the recording was ample an expander can bring that piece of audio back to life.
DeEsser is also a form of dynamic processing control and can be achieved using multi band compression in many cases. Some DeEsser units will create an EQ spike to aid in detection of the unwanted frequency range.