The term “activist judge” is largely a pejorative term in our political discourse today. It is a term that can be used by anyone to malign a judge who makes a “wrong” decision. However, it is a term that is more commonly used by conservatives to attack liberal judges.
An activist judge is, generally speaking, a judge who bases important decisions on their own ideas about what the law should be, rather than on the letter of the law as it is written. This particularly applies to constitutional decisions. An activist judge finds rights in the Constitution that are not clearly and explicitly listed there. The judge then uses those rights to actively overturn laws that have been passed by the elected branches of government. A conservative would point to the finding of the right to an abortion in Roe v. Wade as a prime example of this sort of judicial activism.
Federalists would, in general, have been able to accept the idea of an activist judge. To the Federalists, too much democracy was a danger. It was better to give more power to learned people who were not elected by the people. The idea of educated judges providing a check on the elected branches would have seemed like a good idea to them.
Today, I would argue that our attitudes towards judicial activism are simply partisan. We call judges activist when they rule in the wrong ways. Therefore, a conservative sees activism when a judge rules in favor of gay marriage while a liberal sees activism when a judge rules that corporations have the right to give unlimited money to organizations that support political candidates. In short, we see our judiciary as another battleground for partisan forces.