There are many factors that influence court decisions. There are not supposed to be, but there are.
Ideally, the only thing that will influence the decision a court makes is the law. The courts are supposed to make their rulings based solely on the law. In the case of the Supreme Court, for example, decisions on constitutional law are supposed to be based solely on what the Constitution says on a given issue.
However, judges typically take other things into account. One thing they take into account is partisan politics. An example of this is Bush v. Gore, the court case that decided the 2000 presidential election. It is worth noting that the five conservative justices voted for Bush while the four liberals were in favor of Gore’s position. Another thing that the justices take into account is the interest of the judicial branch. An example of this can be seen in the “Obamacare” case. There, Chief Justice Roberts seems to have gone out of his way to avoid overturning Obamacare. He presumably did so because he did not want the Court to get blamed for throwing out such an important law that had been passed by the elected branches.
A number of factors, then, can influence the decisions that courts make.
A number of factors influence court decisions. The question references only "court" decisions. It can logically be assumed that the question is specific to decisions of the United States Supreme Court. If "court" is defined as trial courts, both criminal and civil, then a multitude of factors can influence decisions, especially given the variables involved, including whether the defendant waives his or her right to a jury trial in favor of a bench decision rendered by a judge. In a jury trial, 12 individuals of varying levels of education and representing multiple ethnicities and genders must come to an agreement for a conviction. Absent a consensus, a "hung jury" is declared and the defendant is either tried again with a new jury or the charges are dropped and the defendant is absolved of any responsibility for the alleged transgression.
Now, assuming the question is specific to decisions by the U.S. Supreme Court, the factors that influence final decisions are, again, varied. The Supreme Court, when at full strength, is comprised of nine sitting justices, all serving life terms, which insulates them from outside pressures with respect to court decisions. While that protection from outside influences exists, however, psychological pressure is routinely asserted by outside forces, such as when large demonstrations take place outside the Supreme Court building intended to influence the individual justices. Additionally, individual justices may feel pressure or be overly influenced by political offices, such as in the United States Senate or in the White House. The Judicial Branch of the United States Government is supposed to be completely independent from the other two branches of government, but, when push comes to shove, the justices are human and are often sensitive or receptive to various influences.
The nine justices of the Supreme Court, as with a jury, represent varying backgrounds, ethnicities, and ideological perspectives. They are unique individuals who bring different judicial philosophies to the job, and they are frequently deliberating on issues that most certainly were not discussed at the Constitutional Convention, such as abortion. While the primary responsibility of the Supreme Court is to consider and rule on the constitutionality of lower court decisions and procedures, including by law enforcement officials, there is no consensus on how to interpret the Constitution. "Originalists" like the late Justice Anton Scalia will always attempt to interpret decisions through the prism of the closest readings possible of Founding documents, including the Federalist Papers.
What makes their job so difficult, however, is that they must also interpret the intentions of those making laws between 1787 and today. Having worked on legislation quite a bit in the U.S. Congress and written so-called "statements of managers," the question of congressional intent is very important in court deliberations. "Statements of Managers" are reports written by congressional staff responsible for specific issues and legislation and articulate, to the extent possible, the meaning and intent of the legislation. When the Judicial Branch is considering the constitutionality of decisions, procedures and laws, it always, or should, review those reports. Congressional intent, then, as well as interpretations of the Constitution written hundreds of years ago under very specific circumstances represent potential influences on court decisions.
The myriad perspectives on the Supreme Court, when combined with the above variables, all influence court decisions. It is considerably more complicated than some may assume, and considerably less tidy.