One often heard phrase relevant to this question is the Constitution as a "living, breathing document".
Proponents of judicial activism would tend to agree with this phrase. It means that the Constitution has a dynamic meaning, based on the time in which society interprets it.
For example, many people would argue that the term "liberty" means something different at the time the U.S. Constitution was written as it means now. Indeed, the 14th Amendment has been used as justification in several high profile cases recently, such as Obergefell v. Hodges. The relevant portion of the amendment reads:
... nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
In Obergefell, Justice Kennedy, writing for the majority, noted that the relationship between liberty and equality is central to the meaning of the Amendment, and that accordingly gay couples cannot be denied the right to marry.
They ask for equal dignity in the eyes of the law. The Constitution grants them that right.
Few people in 1787, when the Constitution was written, would have said that liberty and equality encompasses the right for gay people to marry, but most polls today show that a majority of Americans support the decision. Critics would call this interpretation a form of judicial activism, and would say instead that the Constitution should be amended through a legislative process if society wants to make it unlawful for a state to deny gay couples the right to marry.
These phrases are usually associated with the Supreme Court, though they describe philosophies that could be held and exercised by lower court judges as well. Judicial activism means that justices can and should broadly exercise their own opinions and convictions in decisions. On the other hand, critics argue that by doing this, judges were basically reading their own opinions into the Constitution, a practice likened to "legislating from the bench." In fact, most of the landmark decisions in Supreme Court history have had this charge leveled at them, and the charge of judicial activism can often serve as a shorthand for criticizing decisions with which one does not agree.
Judicial restraint describes a general unwillingness to take a broad or novel interpretation of the Constitution or law on the one hand, and to overturn established precedent on the other. Judicial restraint also means that judges are reluctant to overturn laws made by Congress. Practitioners of judicial restraint are unwilling, in short, to create new interpretations of the Constitution through their decisions. Critics of this approach argue that it binds the people of today to precedents that emerged during very different social contexts, preventing the Constitution from being responsive to modern interests.