Sleeping bags are protective bags to keep people warm when camping outside, they are essentially protective blankets that are sealed usually with a combination of a zipper, Velcro and drawstring. Sleeping bags are essential to any camping trip as they insulate your body from the cold of being outdoors, your tent will keep the wind and rain off you but it's your sleeping bag that really keeps you from getting too cold.
There is some debate as to whether synthetic insulation or down is better for a sleeping bag. Synthetic insulation will dry out if it gets wet and doesn't readily absorb water it's also very resilient whereas down must be kept dry however it does tend to insulate better and is lighter than synthetic insulation. A double sleeping bag is just a very wide sleeping bag and is ideal for couples.