One of the most important features of AIR is the signing of applications, which allows users to know who built an application so they can decide whether to install. Adobe strongly recomends the use of a certificate issued by a well-known, trusted certificate authority (CA) for any application that is going to be distributed to the public.
The Adobe Developer center has a number of great articles that will take you through the all of the steps to digitally sign your AIR application.
One of the first steps to take is to acquire a certificate. To help make that easier, one of the most popular CAs, GlobalSign, is offering an end of year promotion for their certificates.