Equity is branch of legal jurisprudence that allows a court to make decisions based on what is "right" or "just." Things like injunctions, stays, and similar legal devices are all apart of equity. As opposed to equity, law required courts to follow precedent and rigid procedures. In England there were separate courts for law and equity. In the US, the Judiciary Act of 1789 gave federal courts jurisdiction over law and equity. In 1822, rules were set out for federal courts that referred them to look at what English courts of chancery were doing if they were uncertain how to act.
In a time of such distrust between England and the US, following the War of 1812, why would the Supreme Court not create its own formulas for equity instead of referring courts to what England was doing?
Outside of Louisiana American law is based on English law, with English Common Law and the Law of Equity being used everywhere else. Given that, for a very long time American courts made reference to English precedents given as their courts had applied the same basic set of legal principals for a very long time. Indeed, this is still the case as you will find that such principals as The Rule In Shelley's Case, or the Rule against Perpetuities are widely applied in American jurisprudence but are English precedents. There are many other such examples. Some State constitutions expressly adopt English Common law by reference to year and even the then sitting monarch. So this was a natural way to do adopt a set of principals and procedures in a way that could be readily adopted and understood by practitioners of the day.