Dynamics is the branch of classical mechanics concerned with the study of forces and their effects on motion. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.
The 'dynamics' of music is the process of playing parts of the score or song louder or softer, although, sadly, there's a lot of rock that doesn't do any of that.
In printed music ... the sheets that musicians use to play from ... the 'dynamics' means the signs and symbols on the sheet that tell each instrument when to play loud and when to play soft. In formal music notation, there are actually symbols for 8 or 10 different levels of loudness, plus other symbols that tell the player when to change, how fast to change, and how far to change.
