It means Sport Injection

SI was used on hondas first Fuel Injected car back in the old CRX. all civics and CRXs were Carburated until 85 i believe when honda introduced fuel injection, know as SI. Prelude SI and CRX SI debuted that year.

ever since then it has been used to denote the upper Trim models, such as CIVIC SI, CRX SI, etc.

Its almost as popular as what TYPE-R stands for, "type Racing".