Isogeometric analysis is a means of doing finite element analysis over boundary representation models; FEA is used to physically simulate materials, and usually

Isogeometric analysis is a means of doing finite element analysis over boundary representation models; FEA is used to physically simulate materials, and usually requires a polyhedral mesh (a mesh where the elements are 3D, instead of the "normal" kind where the elements are 2D polygons). IGA is a way to skip conversion of your b-rep to a mesh while doing that sort of simulation.