You cannot use Cydia to jailbreak a phone, because you must jailbreak the phone before installing Cydia. Certain jailbreaking tools automatically install Cydia after jailbreaking the phone, while others give the user the option to install it.
Cydia is an application that allows you to download applications not carried by the Apple app store. The application is compatible with iPhones, iPads and iPod Touches, as of April 2015.
When Cydia launches, it prompts you to select whether you're a user, hacker or developer. User is the most user-friendly option, while hacker and developer provide more abilities, such as interacting with the device's command line interface.