Common law is the law developed by judges. The basic premise is that following the Norman conquest William I sent out judges to establish law and ascertain common practice. They then (allegedly) met up at intervals and adopted the best 'common' (local) laws from around the country which became national law. This process has continued so that common law (as defined in the courts) still reflects the law as defined by precedent.
Equity is the principle first developed in the King's inner chambers and is based upon an idea of fairness. The common courts are based upon precedent which isn't the same.
The House of Lords issued a 'practice statement' in the 1960s saying that it (and only it) could break with precedent and disobey it's own previous judgements but that this would be a rare and important step to take because consistency and reliability of law is more important than equity (fairness).
So briefly, equity is fairness and common law is precedent.
Hope that helps.
Cheers,
Stuart