Why is there an extra pair of rails in the center of the track (usually on bridges)?

The reason why these rails are used on bridges is, as has been explained, to prevent a derailed rail vehicle striking and damaging the bridge itself. If this was to happen it could compromise the structural integrity and strength of the bridge, which is clearly not a good thing to happen.

Tight curves do also have check-rails or guard-rails on them to mitigate the consequences of a derailment. But if a rail vehicle does fall off and go tumbling down the embankment and into the river it would be a bad outcome, but it wouldn't cause any further damage to the infrastructure.

They're called "guardrails." Their purpose is to keep a derailed car more or less in line with the track, to prevent it from hitting the bridge structure and damaging it, thus leading to compromise safety, as the car moves along in a train.

a extra set of tracks to keep the train on the track if it derails this always does'nt work

to keep the train on the tracks