Binding energy is the energy required to separate two objects, presumably bound together by some force. The concept and term is used in respect to nuclear reactions, ionization, chemical reactions, but also applies to items bound together by gravity. Given that it refers to energy required, it is generally expressed as a negative number, and when the opposite is done, i.e., the two unbound objects are bound together, binding energy is released, and this is expressed as a positive number.
In the nuclear case, transformations that release binding energy (e.g., fusion) are of detailed interest due to their role in powering stars and some transients. Uncovering fusion reactions plausibly triggered by the Sun's internal temperature and releasing significant energy was a big step in developing current models of stellar structure.
In fact, the binding energy of gravity can be as significant, e.g., during star formation, or when involving a compact object.