A Di Box basically turns an unbalanced audio signal into a balanced signal. Which effectively cleans up the signal reducing background hum (usually from ground) They can be passive (unpowered) or active (powered). Powered DI boxes usually require a 9v battery or can sometimes receive phantom power from a mixing desk such as the Allen and Heath Zed 24.
There are many applications of theses boxes and will vary from application to application.
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Matt Cooper 