Umm... dude, it's A N A L O G. As in, not digital. Instead of being a dick about it, I'll do my best to explain this to you in a way that will hopefully make everything clear to anyone from a complete n00b to someone who kind of knows what they're talking about, but isn't quite sure:
Purely analog mixers are analog all the way through, meaning at no point is the audio signal from the microphone/pre-amp converted to a digital signal (1's and 0's). It passes signals through fluctuating voltage in wires.
In order to pass audio into the computer, at some point you need to convert the Analog signal to a Digital signal. When you hear about people talking about 'interfaces' or 'A/D converters', this is what they're talking about. Some interfaces (like, for instance, the Digi002) have pre-amps, converters, and a digital mixing console all built into one unit!
So, if you have a nice big analog console, and you want to use it with your computer, you need to purchase some sort of converter (Apogee makes some extremely nice ones, M-Audio has a decent inexpensive one called the Delta 1010) to convert the audio from analog to digital, and/or from digital to analog. Think of the converter as a translator between your mixer's language (analog) and your computer's language (digital). If you want either of them to be able to 'talk' to eachother, you need a 'translator' (converter).
Does that help?
*edit: Firewire is a digital communication method, used for connecting things like external Hard Drives, interfaces, digital consoles, etc. It has a limit on the amount of digital data it can pass, but it's much higher than ADAT is capable of. 'ADAT' (an optical connection, also called 'Lightpipe') is another digital communication method which audio equipment uses between themselves to pass digital data as well, although it's mostly limited to 8 channels of data (depending on the device, I believe the max is 8 channels of 24bit/48khz). Originally used with ADAT machines (tape-based digital recorders), it's primarily used as a digital transfer method in a digital recording studio, either to communicate with external gear, or to add channels of pre-amps to your interface (I use it to connect an 8-channel Pre to my Digi002, to get me 12 preamped channels of I/O).
*edit2: it took me a while to post this, so xstatic's post wasn't there when I started typing
*edit3: Also also, I wouldn't go boasting about using a $20k yamaha console: many of the people in here have worked on $100k-1mil. + consoles at one point or another
Look for names like SSL, Trident, and Neve and you'll see what I mean