The Background() application plays a sound prompt, but listens for DTMF input. Asterisk then tries to find an extension in the current dialplan context that matches the DTMF input. If it finds a matching extension, Asterisk will send the call to that extension.
The Background() application takes the name of the sound prompt as the first parameter just like the Playback() application, so remember not to include the file extension.
One problems you may encounter with the Background() application is that you may want Asterisk to wait a few more seconds after playing the sound prompt. In order to do this, you can call the WaitExten() application. You'll usually see the WaitExten() application called immediately after the Background() application. The first parameter to the WaitExten() application is the number of seconds to wait for the caller to enter an extension. If you don't supply the first parameter, Asterisk will use the built-in response timeout (which can be modified with the TIMEOUT() dialplan function).