The extension comes from Lance Fetters...
Applications are not designed to be run in the background (as Apple does not permit it). Thus some applications may not behave correctly when placed in the background. Unfortunately, this is something that Backgrounder cannot resolve; the application itself would need to be modified. Please keep this in mind.
Also note that applications may use the suspend/resume methods to perform important tasks, such as saving preferences. If the application is not properly terminated, these tasks may never be run. For such applications, if your phone crashes or if you force power-off (by holding the power and menu/home buttons), your settings/information for that application will not be saved. Always make sure to properly shutdown such applications (by disabling backgrounding when the application is no longer needed).
While this extension should work for all applications, it is recommended to use it only for background-enabling AppStore applications (which, again, are not allowed to include backgrounding code). If you wish to run a non-AppStore 3rd-party application in the background, it is suggested that you contact the author of the application and request that proper background support be added.
Once you have installed backgrounder you can enable backgrounding from an application by pressing and holding the menu/home button until a message pops-up stating "Backgrounding Enabled".
Backgrounder can be installed from Cydia Installer. We will provide a more in depth tutorial on how to use it shortly.