DI is short for 'direct input' and it means you take a direct signal from a source. Usually a DI will be used for recording guitar, bass, and keyboards.
"Why should I use a DI, when I have a perfectly good amp that can be mic'd?"
Good question. If you like to mic up your amp, go ahead and do it. As a secondary back up, I'd suggest splitting the signal and tracking a DI along with your amp. You'll get a nice clean track along with your amp track to work with when you mix. Think of it as a safety net in case the amp track doesn't work out. Maybe the mic didn't capture the tone you wanted, but the performance was epic. If you tracked a DI, then the performance has a chance to be relived & re-amped!
Re-amp your performance with the DI track. You can now play back the clean DI track and feed the signal into your amp. Move the mic around until you find the tone you desire. Now you have lots of options with minimal effort and you look like a seasoned pro. There are other options like using the DI track with amp emulated software. This way you can shape your tone with digital ease. There are so many possibilities with digital software that you can try out many different sounds to hear what works best for your mix. There are so many options at the fingertips of engineers, this is a great time in musical history. Take advantage of the DI and begin to explore what your music can become.