Gillette's space is

Retropharyngeal space, situated behind the pharynx and extending from the base of the skull to the bifurcation of the trachea. Space is divided into two lateral compaments (spaces of Gillette) by a fibrous raphe. Each lateral space contains retropharyngeal nodes which usually disappear at 3-4 years of age. Parapharyngeal space communicates with the retropharyngeal space. Infection of retropharyngeal space can pass down behind the oesophagus into the mediastinum. (Ref: Diseases of ear, nose and throat, PL Dhingra, 7thh edition, page no. 299)