On the supreme court there are nine total justices. This number was previously six. It was changed over time. It was at one point ten. There is one chief justice and eight associate justices.
The supreme court is the highest court in the land. They are the final court. When cases are appealed they end at the supreme court. Usually many cases don't make it all the way to the supreme court.
The supreme court is limited by checks and balances however. The president has to choose justices. This gives him influence over the supreme court. Congress also has influence over the supreme court because the senate confirms justices.