From an audio engineer perspective -
Dynamics are the variations in level/volume in the audio signal and musical partd like a recording of piano, vocal tracks or guitars range from loud to soft over the course of, say, a song. The upper and lower limits of that variation {the difference between the loudest and softest levels} is the Dynamic Range.
The previous graph showing wave signals is a good representation of dynamics. When we look at audio waveforms the ability for wave forms to fully express themselves without being cut off by any interference or compression, the waves will vary greatly from low wave peak to high with all the instrumentation and such presented in the music. Often times, limiters, compression, and gear like mics, dacs, etc - can cut off the full potential of a audio wave. Thus limiting it's dynamic range.
Actually, this is often done with music set for radio. You can see songs mixed for radio fall within a set range and have their upper and lower wave forms just cut off. They're compressed specifically to enhance loudness so the track appears to sound "better" for listeners on the radio. What's actually happening is much of the musician and their instruments are being cut off from fully expressing their voicings. So - something with better dynamics and dynamic range, will have the ability to offer a more complete voicing of the original instrument. A songs specific dynamic range is its highest peak wave point, to it's lowest peak wave point.
The ability for gear such as headphones and speakers to have good 'dynamics' generally is the response time of the transducer being moved and how rapidly it can articulate each waveform to it's true complete form. To help example this - picture a normal paper cone speaker. You watch the cone move back and forth very quickly to the music. If you're listening to a track that has many instruments and sounds all over the frequency range going all at once, that speaker cone is moving as fast as it can to reproduce every single audio signal from low powerful waveforms to high very rapid waveforms. In many cases it is not accurately displaying all of those sounds - because it PHYSICALLY can't. The cone is being pushed out by air to reproduce one part of the waveform and then relaxes back in, there is physics involved in how fast it needs to move to reproduce each frequency accurately. If the speaker cone is flexing outward at this current moment, it's not moving inward. Thus, in complex passages, there are some frequencies that are requiring the speaker to move at s certain pace that's very rapid, and others that's more slow. It cannot achieve both at the same exact second because its physical shape can only move to a certain maximum speed and capacity.
Even with low end reproduction, you can have a powerful cone that's pushing large volumes of sir to reproduce low end frequencies very well, but s flute is playing at the same time in the song, if the speaker is flexing outwards to play the low end note, low and slow, it's not also properly flexing super rapidly for the high note. Thus, you get frequencies of sounds that might be in the music but simply not being reproduced by the speaker.
This is why we developed different cones or transducers to play different parts of the frequency range at the same time. So more of the dynamics of the music can be expressed all at once because one speaker isn't responsible for the full range of sounds which it literally and physically cannot reproduce all at once no matter how good it is.
So, for something to have good dynamics, it has the ability to properly display the sounds of the quietest instrument to the loudest, the fastest to the softest - all at the exact same moment - as is displayed in the original recording.
- which, just to add to the information dump, often times the microphones we record with aren't even fully picking up all the dynamics of even a single instrument it's recording. It too has diaphragm that is moving in physical space this has its limitations of how quick or slow it can move and the more sounds it's trying to pick up at once - the more physically impossible it becomes for the microphone to move to register all of the sounds. Thus, even recordings are missing much of true dynamic range. It's just physics, we have not yet s perfect solution. Just an ever expanding quest to get better recording and then playback