PhoneGap apps can provide a login functionality to another web application by calling making an HTTP request to some URL that authenticate the passed user credentials. The main difference is that in PhoneGap this request typically done in an AJAX style rather than a full page submission like is common for a web browser.
In both cases though the goal is to establish a session with your application server so that subsequent requests to the app server can determine who is making the request and if that user has permission to do what the request is asking for.