Because the switch has either failed or come off it's mounting. There is an outside chance, if there has been work around the handbrake lever/centre console, that the switch wires might have become trapped and could be shorting out.
it has a sticky handbrake switch
If the handbrake light on your Peugeot 206 stays on, it could indicate that the handbrake is engaged or that the brake fluid level is low. Additionally, there may be an issue with the handbrake switch or a fault in the braking system. It's advisable to check the handbrake and fluid levels first, and if the light persists, consult a mechanic for further diagnosis and repair.
handbrake light
The handbrake light is also the 'low fluid' warning light. It is connected to the handbrake as that ensures that it is checked every time you use the handbrake. If it remains on all the time, then check the brake fluid and top up if required. If the fluid is ok then it is probably the switch on the lever and is adjustable.
The fuse for the handbrake light on a VW T5 is typically located in the fuse box, which is found under the dashboard on the driver's side. You can identify the specific fuse for the handbrake light by consulting the fuse diagram usually found on the inside of the fuse box cover or in the owner's manual. If the handbrake light is illuminated despite the handbrake being disengaged, checking the fuse is a good first step for troubleshooting.
Because you probably still have your handbrake on. If not, than you need to see the car-doctor.
it means your handbrake is on
usually a sticky switch on handbrake, had any welding recently ?, worn shoes ?
your switch that tells the car that the brake is off is defective
Release the handbrake
Either the switch (on the handbrake) is sticking or you have a short circuit, usually caused by corroded wires or connections.
Either your handbrake switch is broken and will not turn off or you have low brake fluid.