How is the word "right" commonly used, both correctly and incorrectly?
The word "right" has many meanings, as noted in the dictionary. It can be used to mean the opposite of the left or back side; something lawful or morally correct; true; acceptable or proper; to the highest degree; restored to its proper place or condition; or an expression of agreement. Today it is often even tacked on to a sentence as a kind of slang tag question, as in "I know, right?"
Since this question is under the topic of business; however, you probably want some amplification about the term "right" as it is used so frequently in the political and business arena.
The Bill of Rights is a list of Constitutionally mandated rights which every citizen of the United States has; in general terms, this is a list of rights citizens have from the government (such as the right to bear arms, to be tried by a jury of peers, to be free from unlawful searches and seizures). It is common today, however, to see the things given by the government as rights when perhaps they are technically not (such as welfare, food stamps, and health care).
Note the following three definitions from the dictionary listing cited below:
That which is just, morally good, legal, proper, or fitting.
A just or legal claim or title.
Something that is due to a person or governmental body by law, tradition, or nature.
It is clear that the line between what is an actual Constitutionally protected right and what the citizenry feels it needs or deserves from its government has moved significantly in the last several centuries. Today the word "right" is often equated with fairness and equality rather than any legal determination based on the Constitution.