What is Political Question?

Legal Definition
In American Constitutional law, the political question doctrine is closely linked to the concept of justiciability, as it comes down to a question of whether or not the court system is an appropriate forum in which to hear the case. This is because the court system only has authority to hear and decide a legal question, not a political question. Legal questions are deemed to be justiciable, while political questions are nonjusticiable. One scholar explained:

The political question doctrine holds that some questions, in their nature, are fundamentally political, and not legal, and if a question is fundamentally political ... then the court will refuse to hear that case. It will claim that it doesn't have jurisdiction. And it will leave that question to some other aspect of the political process to settle out.

A ruling of nonjusticiability will ultimately prohibit the issue that is bringing the case before the court from being able to be heard in a court of law. In the typical case where there is a finding of nonjusticiability due to the political question doctrine, the issue presented before the court is usually so specific that the Constitution gives all power to one of the coordinate political branches, or at the opposite end of the spectrum, the issue presented is so vague that the United States Constitution does not even consider it. A court can only decide issues based on law. The Constitution dictates the different legal responsibilities of each respective branch of government. If there is an issue where the court does not have the Constitution as a guide, there are no legal criteria to use. When there are no specific constitutional duties involved, the issue is to be decided through the democratic process. The court will not engage in political disputes.

A constitutional dispute that requires knowledge of a non-legal character or the use of techniques not suitable for a court or explicitly assigned by the Constitution to the U.S. Congress, or the President of the United States, is a political question, which judges customarily refuse to address.
-- Wikipedia
Legal Definition
Subject matter that the Supreme Court deems to be inappropriate for judicial review because discretionary power over it should be left to the politically accountable branches of government (i.e., the President and Congress). Thus, the courts will leave constitutional questions on such matters to be resolved in the political process. Courts will usually find a matter to be a political question on one of two grounds: (1) the constitutional concern for separation of powers, where the Constitution has already committed the matter on other nonjudicial branches of government for decisionmaking; and (2) prudential concerns which lead the Court to choose to refrain from adjudicating the matter.
Legal Definition
Questions of which the courts of justice will refuse to take cognizance, or to decide, on account of their purely political character, or because their determination would involve an encroachment upon the executive or legislative powers; e. g., what sort of government exists in a state, whether peace or war exists, whether a foreign country has become an independent state, etc. Luther v. Borden. 7 How. 1, 12 L. Ed. 581; Kenneth v. Chambers, 14 How. 38, 14 L. Ed. 316; U. S. v. 129 Packages, Fed. Cas. No. 15,941.
-- Black's Law Dictionary