In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. For example, the fine-structure constant is a coupling constant that determines the strength of the electromagnetic force. In quantum relativistic units, such coupling constants are pure numbers, much like in the case of the fine-structure constant.
If the coupling constant is (much) smaller than one, the theory is (very) weakly coupled, and it can be (very) well described by perturbation theory where the coupling constant plays the role of the expansion parameter; this is the case of quantum electrodynamics, for example. If the coupling constant is of order one or larger, the theory is strongly coupled; for example, quantum chromodynamics is strongly coupled.
In string theory, each perturbative description of string theory depends on a string coupling constant. However, in the case of string theory, these coupling constants are not pre-determined, adjustable, but universal parameters, but rather dynamical scalar fields that can depend on the position in space and time and whose values are determined dynamically.
Strong-weak duality is an equivalence between a strongly coupled and a weakly coupled theory.
