Someone will probably explain it better ; DI ( Direct input ) is where you have a cable going from your amp ( if it has a DI socket) into an audio mixer.
Some multi effects units have a DI socket , which means that in theory you could plug the cable from your multi effects unit into the audio mixer directly without bringing your amp to gigs / rehearsals . Also, if you did use the multi effects unit , there is a button on the unit giving you the option of ' straight bass ' without effects if you prefer.
DAW , is digital audio workstation . This is a device where you plug your instrument into it which allows you to record onto your computer