What is Time constant?

Example 30.9 (A flash unit’s numbers)

A photo flash charges $C = 800\,\text{µ}\mathrm{F}$ through $R = 1.0\,\mathrm{k}\Omega$: $\tau = 10^3 \times 8.0\times10^{-4} = 0.80\,\mathrm{s}$, so the “ready” light — wired to trip at $95\%$ — waits $3\tau \approx 2.4\,\mathrm{s}$: the whine of the hook. Fired through the flash tube’s mere $0.50\,\Omega$, the same capacitor empties with $\tau' = 0.40\,\mathrm{ms}$: two thousand times faster out than in.