Generally speaking, binarity relates to the fact that exactly two values are available for a given choice or decision.
In decompositional semantics, binarity is a property of a feature. A feature is said to be binary iff it can take only one of two values. For example, the lexical feature [concrete] can only assume the values [+ concrete] and [- concrete].
In syntax, binarity is often (a priori) regarded as a property of constituent structure. In a binary structure, each constituent is split up into at most two daughter constituents.