Why do a bulb connected in circuit glow for while and then go off when key is witched off.

In case of an incandescent bulb, the whole operating principle of the bulb is based on getting the filament really hot, hot enough to glow. When you cut off the current, it stops heating the filament, so it cools down fairly rapidly, but there may be enough residual heat for a faint glow lasting a little while afterwards.

If it's a CFL bulb or an ordinary fluorescent bulb, the "white" color we see is produced by a fluorescent coating on the glass of the bulb, which converts some of the invisible ultraviolet light produced by the excited gas atoms into visible light. When you cut off the current, you stop exciting the gas atoms and thus stop producing new ultraviolet light, but there may be enough residual excitation in the material to keep glowing for a little while afterwards