A reason is a sentence (or detail) supporting a claim, whether the main claim or a minor one.
Example: The emancipation of Russian peasants was an empty gesture (claim) because it did not improve the material quality of their daily lives (reason).
Example: TV violence can have harmful psychological effects on children (claim) because those exposed to lots of it tend to adopt the values of what they see (reason).
Claims and reasons can get confusing, because a reason is often supported by more reasons, which makes the first reason a claim in its own right. In fact, a sentence can be both a reason and a claim at the same time, if what it states supports a claim and is in turn supported by another reason.
Example: TV violence can have harmful psychological effects on children (claim 1) because those exposed to large amounts of it tend to adopt the values of what they see (reason 1 supporting claim 1 / claim 2 supported by reason 2). Their constant exposure to violent images makes them unable to distinguish fantasy from reality (reason 2 supporting reason 1 / claim 2).
Reasons can be based on reasons, but ultimately a reason has to be grounded on evidence.