A fire blanket is a sheet of fire-resistant material, typically fiberglass, that's used to smother small fires by cutting off their oxygen supply.
Fire blankets are most effective on small, contained fires, such as:
Kitchen Fires: Grease fires in pans, small appliance fires.
Clothing Fires: If someone's clothes catch fire (remember the stop, drop, and roll technique, then use the blanket).  
Small Waste Bin Fires: Fires in trash cans or recycling bins.