How some clock needles emit light at nighttime?

They use phosphors chemicals
Zinc sulfide and strontium aluminate are the ones that are most commonly used in glow-in-the-dark products

Phosphorescence is actually a very interesting phenomenon, that can only be fully understood with knowledge of quantum mechanics. Unlike luminescence, when a photon is absorbed and then re-emitted by an electron on the timescale of nanoseconds, the electron (excited by a photon) enters a state with high spin multiplicity. These states only can only return to the lower energy state through "forbidden" quantum mechanical processes. These "forbidden" processes do occur, but are kinetically unfavorable and so progress at a much slower rate. This is how the substance can continue to emit photons for several hours after being illuminated.

Also, many years ago, radioluminescent paint was used on clock hands. This process is a little easier to understand - the radioactive decay of isotopes (normally tritium) excites electrons to a higher energy state, which then radiates photons as they spontaneously emit down to a lower state. This is a much quicker process (again on the scale of nanoseconds), but the energy source is always there to continually excite the electrons. This obviously was dangerous for the workers whose job was to paint the clocks.