Wat is Von Neumann stability analysis, CFL condition?

Von Neumann stability analysis substitutes a Fourier mode $U_j^n = g^ne^{\mathrm ij\xi}$ into a constant-coefficient scheme and requires $|g(\xi)| \le 1 + O(\Delta\tau)$ for every frequency. The CFL condition (Courant, Friedrichs and Lewy, 1928) is the resulting restriction of the time step by the space step for an explicit scheme.