Though the same current flows through the wire and the filament of a bulb, yet only the filament glows. Why?

Hint: We need to understand the mechanisms involved in the glowing of a bulb with a filament inside it. The factors which cause the filament to glow and the reasons why the wire does not glow in the same condition can be discussed to solve the problem.

Complete step by step answer:
A tungsten bulb lights up when a current passes through it. The same current when passing through a wire does not glow or heat to that extent. We know that the heating of a material is dependent on the resistance of the material through which the current flows.
The tungsten is a highly resistive material. When the current passes through the tungsten filament, the material heats up and turns red-hot. This is the glow we see as light from a tungsten filament bulb.
The wire that connects the circuit in a household is supposed to transmit currents without much loss of energy. To succeed in this target, the resistance of the wire used in electrical circuits are kept the minimum. As a result, it does not heat up to any extent that can produce lighting effects.
This is the reason why the tungsten filament bulb glows when a current is passed through it and the wire used in the circuit does not act in the same way as that of the bulb.
This is the required solution.

Note: The tungsten is the best elemental material which can turn into a red-hot in the available resources. The tungsten can produce glow at very low currents as it is very highly resistive and thus heats up to thousands of degrees Celsius in a few milliseconds.