In royal families, the crown goes to the oldest child. That's the heir. The "spare heir" is the next child who would ascend the throne should something happen to the heir. In the UK, when William becomes King, Prince George is the heir. His brother or sister, who will be born in April, will be William's spare heir. Harry was the spare heir until Prince George was born.
Aristocratic wives were once told they needed to provide an "heir and a spare heir" at least.