like Nimrod said, an active DI includes amplification and other active components.
ussually, a passive DI can be used for louder sources like keyboards, active guitars, samplers, drum machines etc,
and an active DI would be used for guitar / bass pickups etc.
if you take a low level signal from a passive DI and amplify it in a mic preamp
you will get that preamp's charchter on the channel.
sometimes the signal is too thin for a passive DI, but it depends on the source.
the advantage of passive is less components = cleaner signal path.