It's the highest court in the land. An entity with so much influence over federal law that the appointment of a new justice can cause an almost existential reaction among lawmakers and the public alike. How is it possible, then, that Alexander Hamilton thought of the Supreme Court as "beyond comparison the weakest of the three departments of power"?
The United States Supreme Court appears in the Constitution, but it gets a light touch. In fact, not much is said about it besides the fact that there has to be one, and that it has to have a chief justice. Not a word about the number of justices, nor the the specifics of their term. Only that justices shall hold their offices during "good behavior." This has been interpreted to mean "for life." There is the option of impeachment for justices exhibiting "bad behavior," but only one has ever been the subject of it. Justice Samuel Chase was impeached by the U.S. House of Representatives in 1804 for apparent partisan leanings, but was acquitted by the Senate and permitted to remain on the bench.
It's Congress that establishes the details of the Supreme and lower courts. They set the bench at nine justices (though we've had as few as six and as many as ten) and establish the many district courts and courts of appeals. The Judiciary Act of 1789 even gave the Supreme Court the power to issue writs of mandamus -- a court order that can command a government official to do their established job. And it is that very Act that eventually resulted in the SCOTUS becoming the powerful entity it is today.
In 1803 in the SCOTUS case Marbury v Madison, Chief Justice John Marshall ruled, among other things, that the court did not have the Constitutional power to issue these writs. In other words, Justice Marshall invalidated a statute established by Congress. In doing so, he established judicial review, the very principle that makes the Supreme Court as powerful as it is today. It is, essentially, the ability to rule on the constitutionality of law, to uphold constitutionality and strike down laws that are in conflict with the Constitution.
This is in part why, today, a court that leans conservative or liberal causes both consternation and optimism across the country. For many Americans, issues such as abortion access and second amendment rights are paramount. If a case involving these concerns is appealed up to and accepted by the Supreme Court, the court could very well uphold or strike down laws pertaining to these issues. For those, however, who see these justices as an extension of the President's will, consider Chief Justice John Roberts' words on the matter, "We do not have Obama judges or Trump judges, Bush judges or Clinton judges. What we have is an extraordinary group of dedicated judges doing their level best to do equal right to those appearing before them."