A reason is a consideration which justifies or explains.
Reasons are what people appeal to when making arguments about what people should do or believe. (Those are reasons in the normative sense.) For example, the fact that a doctor's patient is grimacing is a reason to believe the patient is in pain. The fact that the patient is in pain is a reason for the doctor to do things to alleviate the pain.
In another sense of the term, reasons are explanations of why things happened. (These are reasons in the explanatory sense.) For example, the reason why the patient is in pain is that her nerves are sending signals from her tissues to her brain.
Normative vs. explanatory reasons 
Normative reasons (AKA justifying reasons) are often said to be "considerations which count in favor" of some state of affairs (this is, at any rate, a common view, notably held by T. M. Scanlon and Derek Parfit).
Explanatory reasons are considerations which serve to explain why things have happened—they are reasons why events occur, or why states of affairs are the way they are. In other words, "reason" can also be a synonym for "cause". For example, a reason why a car starts is that its ignition is turned. In the context of explaining the actions of beings who act for reasons (i.e., rational agents), these are called motivating reasons—e.g., the reason why Bill went to college was to learn; i.e., that he would learn was his motivating reason. At least where a rational agent is acting rationally, her motivating reasons are those considerations which she believes count in favor of her so acting.
Normative reasons 
Some philosophers (one being John Broome) view normative reasons as the same as "explanations of ought facts". Just as explanatory reasons explain why some descriptive fact obtains (or came to obtain), normative reasons on this view explain why some normative facts obtain, i.e., they explain why some state of affairs ought to come to obtain (e.g., why someone should act or why some event ought to take place).
Epistemic vs. practical reasons 
A common philosopher's distinction concerning normative reasons is between epistemic reasons and practical reasons. Epistemic reasons (also called theoretical or evidential reasons) are considerations which count in favor of believing some proposition to be true. Practical reasons are considerations which count in favor of some action or the having of some attitude (or at least, count in favor of wanting or trying to bring those actions or attitudes about).
Epistemic reasons in argumentation 
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In informal logic, a reason consists of either a single premise or co-premises in support of an argument. In formal symbolic logic, only single premises occur. In informal reasoning, two types of reasons exist. An evidential reason is a foundation upon which to believe that or why a claim is true. An explanatory reason attempts to convince you how something is or could be true, but does not directly convince you that it is true.
- Merriam-Webster.com Merriam-Webster Dictionary definition of reason
- Scanlon, T.M. What We Owe To Each Other. Harvard: Harvard University Press, 1998. p. 17.
- Parfit, Derek (January 23, 2009). On What Matters (forthcoming) (PDF). Rutgers University. Archived from the original on March 31, 2010. Retrieved September 16, 2011.
- Broome, John. "Reasons". In Reason and Value: Themes from the Moral Philosophy of Joseph Raz. Edited by R. Jay Wallace et al. Oxford: Oxford University Press, 2004. p. 28.
- "Practical Reason". Stanford Encyclopedia of Philosophy. Stanford University.