One must understand how a filament bulb works first. The filament heats up due to current passing through (I^2*R losses), and due to its heating, the electrons change their energy states and photons in visible spectrum (and infrared spectrum) are emitted.
More the losses, more would be the light, but at the same time, more would be the heat generated.
So this necessitates that the metal used should have high resistivity (and hence high losses), good thermmal conductivity and high melting point.
A typical filament bulb glows at around 2500 degrees celcius, and tungsten's melting point is above 3000 degrees C.
So, it fits the criteria perfectly.
Light bulbs glows when electricity is passed through the filament.
The filament must have these following properties
High melting point tungsten has melting point of 3422C so it doesn't melt when current is passed it doesn't melt.
Tungsten apart from having high melting point also has high tensile strength. Tensile strength determines how strongly it can be molded into thin wires. Tungsten has low vapor pressure and hence will not produce tungsten vapors when heated. It has low thermal expansion coefficient and hence will not change its shape and structure when heated. This helps the filament not to get separated from the electrodes. Due to all these properties of tungsten, it is used in light bulbs.