What is What μ means?

$\mu$ is the cost, in free energy, of adding one particle at fixed $T$ and $V$. Particles flow spontaneously from high $\mu$ to low $\mu$ — diffusion, osmosis, evaporation, chemical reactions and electric currents are all $\mu$-gradients relaxing. At equilibrium between any two phases or places, $\mu$ is equal on both sides — the third equality (with $T$ and $P$) that governs coexistence. For a classical ideal gas,

adding a particle to a dilute gas lowers the free energy, because the entropy gain outweighs any energy cost — the sign that drives evaporation into dry air. And a battery is a $\mu$-machine: its voltage is the chemical-potential drop per electron between its electrodes, $U = \Delta\mu/e$ — volts are electron chemistry’s exchange rate, which is why cells deliver single-digit volts.