There are two ways the term 'dynamics' is used by audiophiles.
In the vast majority of cases, the word 'distortion' can be safely substituted in the conversation without changing its meaning.
This is because the human ear uses odd ordered harmonics to sort out how loud a sound is. If the system adds odd ordered harmonic distortion during playback, it will sound louder to the ear than it will show on a sound pressure meter. I can offer plenty of examples.
For this reason I am careful to not use the word 'dynamics' when referring to actual changes in volume level. Instead I use the word 'impact'.
So- substituting 'distortion' for 'dynamics' above, its likely the amplifier that many will suggest and they would very likely be correct. If you want to improve the dynamic range of the system, the best way IMO/IME is to work with speakers that do not have compression at high output levels. This usually means going to a more efficient loudspeaker.
My speakers at home are about 98 db 1 watt/1 meter. But I often use amps of 140 watts; in such conditions its pretty well impossible to clip the amps in my listening room, and the speakers don't compress until I get into the threshold of pain.
However I don't normally listen very loud- this results in the system being so effortless that it has no sense of loudness at all- you can't tell how loud the system is playing unless you try to talk to someone standing next to you. This to me is the sign of a good system- one that does not sound loud even when it is. Such systems tend to have more 'impact' as well. The two qualities go hand in hand, even though it might seem counterintuitive.
