Resistance is the ability to not be affected by something. In this case we are talking about circuits, and we are resisting the current provided by the battery. Resistance in a circuit can be anything. This could include a lamp, an appliance, or just about anything that needs power. Resistance is even in the ammeter, although it is incredibly small, and in the voltmeter, which has a huge resistance to not affect the flow of current.
Resistance is vital to a circuit because if there is no resistance the current will flow freely and if fast enough it will heat up the wires. This could eventually cause a fire if not dealt with. This is why we have circuit breakers in houses, to slow the flow of current so it doesn't overheat the wires and cause a huge fire in your house in between the walls where your wires run. The area in between your walls is highly flammable with dry wall and insulation in between it.
This is why Resistance is so crucial to a circuit (and its survival).