Yes, a home furnace can explode. The most common reason for a furnace explosion is when a gas leak occurs and the gas builds up to the point where it explodes. Furnace explosions can also be caused by electrical malfunctions, clogged filters, or overheating.
If you think your furnace might be in danger of exploding, it is best to call a professional to inspect it. If you do experience a furnace explosion, evacuate your home and call the fire department immediately.