Common law is practically the case law covering all certain topics, there is legislation too but that's not what you asked about. Equity often runs with common law, however for certain situations where the common law doesn't provide justice for the individual, equity will be able to step in, and equity will prevail over common law. Think of equity as a shadow, most of the law is covered by legislation or common law, however just where there are gaps, equity will fill in. So examples, may be when common law will award damages (monetary) as oppose to equity awarding specific performance (court rules the party to do a certain action).