Comparison between judicial restraint and judicial activism
According to a report released by The Institute for Justice in 2011, the Supreme Court struck down only 103 (two-thirds of 1%) of the 15,817 laws passed by the Congress from 1954 to 2002. Likewise, state legislatures passed 1,006,649 laws over the same period, and the Court struck down only 452 (less than one-twentieth of 1%).
According to the theory of separation of powers propounded by Montesquieu, the powers of the government must be divided among its three organs - legislature, executive, and judiciary. The three branches of the government must be separate and independent of one another. According to this theory, none of these branches must exercise the powers vested on others. So, this theory is intended to prevent concentration of powers and to provide proper checks and balances. According to Montesquieu, the legislature is entitled to make laws, the executive is entitled to take administrative and policy decisions, and the judiciary is responsible for interpreting and applying the laws made by the legislature.
Judicial Interpretation
When it comes to the powers of the judiciary, the conventional view is that this wing of the government interprets the Constitution and other laws, and applies them. While deciding a particular case, the judge has to interpret the relevant law and apply the same to the facts, in order to reach a verdict. A specific legal provision can be interpreted in different ways. It may also happen that the same law is interpreted by different judges in different ways. While some judges stick to the plain text, others try to decipher the intent of the law and apply it accordingly. There are some judges who rely on precedents (earlier judicial decisions).
Judicial Restraint and Activism
In short, a law can be interpreted in different ways. Judicial restraint and judicial activism are two theories of judicial interpretation. According to the theory of judicial restraint, judges must uphold the laws made by the legislature, and should not try to strike them down, unless they are unconstitutional. He should stick to the meaning and intent of the current law, and should not try to make law. On the other side, the theory of judicial activism refers to that condition, wherein the judge interprets the law, according to his personal view, keeping in mind the needs of the contemporary society. The judge becomes an independent policy maker and exceeds his limit as an interpreter of law. He/she may also strike down unconstitutional laws.

Example 1: The incident happened in a Maltese island during the eighteenth century. There was a judge named Cambro, who witnessed a murder, while looking out of the window. A man was being chased and stabbed by another. The murderer fled, leaving the knife on the victim, as he saw a constable coming from a distance. A baker, who came that way wanted to rescue the victim, and tried to take out the knife. By that time, the constable reached the spot. He found the baker with the blood-stained knife. The baker was arrested and tried before Judge Cambro. The judge sentenced the baker to death, even though he personally knew that the latter was innocent. The conviction was based on circumstantial evidence, that was totally against the baker. In this case, the judge followed the theory of RESTRAINT, by sticking to the law and ignoring personal belief.

Example 2: In Brown v. Board of Education of Topeka, 347 U.S. 483, the Supreme Court of the United States delivered a landmark judgment by declaring state laws that allowed segregation of races in public schools. Though the case comprised several legal issues, the main one was the separate school system for blacks and whites. The state laws were declared unconstitutional, and the earlier decisions that upheld such laws were overturned. This is a classic example of judicial ACTIVISM, as the judges deviated from following the law enacted by the legislature, as they found that the law was unconstitutional. In this case, the judges exceeded their power and interpreted laws, thereby protecting the public interest.
Differences Between Judicial Restraint and Judicial Activism
So, judicial restraint means strict adherence to law, without considering factors like changing needs of the society or fairness. When a judge takes up the role of a legislator and exercises freedom to find new meanings in a law enacted by the legislature, review an existing law, or strike down certain acts and precedents, it is called judicial activism. While judicial restraint tends to be conservative in nature, judicial activism is more liberal.

Power: The main difference between the two theories lies in the extent of power exercised by the judiciary. While judicial restraint limits the power of a judge to interpret law in a broad manner or strike down a legislation; in judicial activism, the judge takes more freedom to deviate from conventional interpretation, so that a law can be applied to a given set of facts. He can overrule laws as well as judgments. According to the philosophy of judicial restraint, there is no scope of interpretation of the Constitution, and changes can be made through amendments only. In case of judicial activism, Constitution can be interpreted in a broad manner.

Scope: According to the theory of judicial restraint, the judge must stick to the laws enacted by the legislature and should uphold them unless they are unconstitutional. In judicial activism, the judge can interpret laws according to the changing needs of the society and prevent injustice.

Intent: While judicial restraint is intended to prevent judges from exercising arbitrary power over the life and liberty of citizens, judicial activism encourages them to exercise more power to shape social policies and to correct injustices, especially when the other wings of the government fail to do so.
Pros and Cons
Here are some arguments and criticisms with regard to these theories. Judicial activism is highly effective for bringing forth social reforms. Unlike legislature, the judiciary is exposed to the problems in the society through the cases it hears. So it can take just decisions to address such problems.

Through judicial activism, the judiciary is keeping a check on the legislature that does not function properly. Actually, it is their duty to solve those matters that plague the society. According to the supporters of this philosophy, the judiciary intervenes only when the legislature fails to do its job. The government may take a long time to enact a law regarding controversial social reforms.

On the other hand, judicial restraint is highly important, even if the legislature fails to work properly. What happens if the legislature executes the functions of the judiciary? It is the people, who have to take steps to resolve that problem, by selecting an efficient legislature.

Judicial activism is contradictory to the concept of separation of powers. It is not fair for one branch of the government to intervene and exercise the power vested with another. When it comes to legislating, the knowledge and expertise of the judiciary may not be sufficient. They may not be competent enough to make major political decisions.

The legislature is elected by the people, and the elected representatives are entrusted with the task of legislating. Unlike the legislature, the members of the judiciary are not elected by the people, and are not supposed to legislate. The judiciary can be arbitrary and unfair. Though the government has three organs, the judiciary has the final say in matters of dispute. There is no other authority above the Supreme Court. So, restraint is advisable while exercising that power.
In short, both the theories of judicial activism and restraint have their own advantages and disadvantages. However, judges striking down unconstitutional laws to protect public interest cannot be considered as encroachment into the domain of the legislature. After all, judiciary is meant for upholding JUSTICE.