The phrase "to support the structure" means to physically or metaphorically help something or someone stay strong, stable, or organized. Full definition
This is an infection of the gums and potentially the other supporting structures of the teeth. (critterdoctor.com)
The recognizable chain has a trusted reputation and a strong support structure for franchises to help its owners successfully run their stores. (businessinsider.com)
We are committed to targets in gender balance, and have a number of support structures in place to promote ethnic diversity and social mobility. (lex100.com)