The definition of a direct box is somewhat subjective. At its core, a direct box does nothing more than accept your instrument's 1/4" banana plug input, which is unbalanced (signal - and ground are combined, meaning ground and hot do not always have the same voltage/current) and output a balanced XLR output (balanced signal + and signal -, with seperate ground).
Most boxes advertised as "DI boxes", however, do more than that simple conversion. Most have a preamp (treble-mid-bass-gain controls) That allow you to mold your bass sound like you would on your amp, and output the result directly to the mixing board. There are also preamps and even combo amps with XLR outputs that can be used to run directly to the mixing board. Both of these however are capable of much more than allowing you to run direct; a preamp will have advanced tone-modelling and the ability to plug into your own power amp and cabs in addition to the XLR, while the combo *provides* the power amp and speakers, and can function as a stage monitor or backline amp while the PA gives you most of your sound.