What does an Audio Interface do?
In the most basic sense, an audio interface upgrades the sound output of your computer. Most computer soundcards + outputs (including the ones that come installed in Macs) are not intended for the higher resolution output associated with music production and DJing.
In addition, an audio interface works in preparing sound that you bring into your computer. If you are recording / sampling into your computer, an interface ensures you'll record quality, high resolution sound.
How does a different number of inputs and outputs effect an interface?
Most computers offer a single input and output. You'll find when you're producing music or DJing, that you'll need more flexibility.
For example, having multiple inputs allows you to record from more than one source. Say you want to record a DJ music mix with talking on the mic. You will want to input the mix and mic separately into your computer, so you can edit and adjust the levels independently in your recording program. Or if you're recording multiple musicians simultaneously, you'll want to record them on separate inputs.
Multiple outputs allow you to send your output to multiple sources. For example, if you want to perform a live set while recording into a recording device, you'll need separate outputs. If you're in a club situation where you have separate master speakers and booth speakers, you'll need separate outputs if you want to adjust the sound of the two speaker sets separately.
For DJs who are mixing solely on their computer (using a program only without a DJ controller or additional setup), a DJ interface adds a 2nd output for headphone previewing. This is feature is essential for DJ mixing.
When will I need an interface?
If you're DJing, most setups include an interface or have an interface built-in. Inquire if the setup you're interested includes an interface.
For music production, you'll probably want a quality interface because you'll need to input sound into your computer. Some, but not all, music production gear comes with interfaces built-in. Inquire to see if any of your music production gear includes an interface, otherwise, you'll probably need one.
What is a MIDI-interface, will I need one?
MIDI interfaces are used to connect older and retro-styled equipment (outboard equipment such synthesizers, effects units, sequencers) to your computer. With most DJ Gear / Music Production Gear, you will not need a separate MIDI-interface. General rule of thumb, if you're device connects to your computer via USB, you won't need a MIDI interface.