You are not sending your login information to Project-GC but instead you allow Project-GC to fetch some of the information bound to your Geocaching.com account from Geocaching.com. This data will be used in accordance with the Geocaching.com API License Agreement. You can at any time you want, revoke Project-GC its rights to fetch your data by visiting Geocaching.com Authorizations.
The authentication used by the Geocaching Live API is based on a standard called OAuth2. This is the same technology that is used by Facebook and Twitter to allow other sites/applications to access accounts. Read more about OAuth2 here, or check out the Wikipedia page for easier reading.
- More information about the API can be found at Geocaching HQ's site about the API