TLDR version: a DI box converts your high impedance, unbalanced, 1/4” jack output from your bass to the low impedance, balanced XLR connector the front of house (FOH) mixing console is expecting.
There are a lot of places, churches most notably, where they are not interested in putting a mic in front of an amp. But if you try to plug your bass into the mixer, you get an impedance mismatch (i.e. sounds like shit) and line noise if your cable run is more than 15ft (i.e. sounds like shit).
The DI box allows you to send the mixer a clean direct signal over hundreds of feet of cable while still feeding your amp on stage. Recording engineers use the DI signal for re-amping or amp cabinet emulations. Churches, festivals, and othe venues don’t want to deal with bass amps and expect you to run directly (DI) into the sound board.
