Given a set of input parameters and a function that outputs the response of a structure, inverse design is the process of estimating adequate values of the input parameters such that the response of the structure meets target properties prescribed a priori. By creating a mapping from outputs to inputs, inverse design thus reverses the conventional forward analysis process wherein one obtains the response of a structure given some input parameter values (a mapping from inputs to outputs).
One should note though that the term "inverse design" can be redundant as the term "design" alone already implies the solution of an "inverse" problem per se.
Consider a simply unsupported beam subject to a uniformly distributed load with some material and cross-section properties. A forward analysis statement yields: "The midspan deflection of this 100x400 mm timber beam is 90mm". In contrast, an inverse design process would render that: "We need a 200x600 beam made of steel to achieve the 20 mm deflection goal specified by the local building code".