"i know analog is converted to digital and back through an analog mixer " -
Sorry, this just isn't true. An analog mixer is called that because it deals with ANALOG signals. There is normally no conversion between digital and analog involved here.
The only exception I could think of would be that SOME analog mixers now include an effects section, most of which now operate digitally.
When you route your analog signals so as to use these INTERNAL effects, that portion of the signal that uses the effects generator gets converted to digital, the effects are applied digitally, then the output of the effects generator is converted BACK to ANALOG and mixed with the (still un-converted) ANALOG main signal, and the summed ANALOG mix is then routed to the outputs of the mixer.
"what good is it? and who would use it, thanks" -
There are advantages and disadvantages to both analog and digital, some of which are real and some of which are only in the minds of people who think that they SHOULD be able to hear a difference, and some of which are just plain BULL.
Even within the same function, there are good, bad and ugly ways of doing the same thing. It's kind of like cars - you can (maybe) get there in a Yugo, if your butt is well padded and you don't mind feeling worse when you arrive than when you left, or you can get there in a BMW 735, travelling in supple leather seats and listening to a soft classical CD (actually HEARING all of its subtle nuances) -
In other words, there is well-designed and poor-designed circuitry in both digital and analog form, and generally the cost reflects which is which. Well-designed analog gear tends to be more expensive than (some) well-designed digital gear.
Analog gear has the advantage of being somewhat simpler to connect in a way, since it doesn't require as much thought to wire. You only need to match levels and impedances between consumer and pro types of gear, and the analog signal will get there.
Digital gear is still evolving, and there are some units that won't interface with others unless you add a "format converter" of one kind or another. Using multiple pieces of digital gear requires connecting not only the "audio" signal, but usually also a Word Clock signal, or the very least problem you get is crackles/pops - sometimes you get NOTHING at all.
The upside of digital is that you can reach a pretty professional level of sound quality in a recording studio environment for less money than the same number of tracks would cost done in analog.
If you're really serious about learning all you can, and don't want to make expensive mistakes buying things that are not compatible with each other, I would second Bear's recommendation about the John Watkinson book - It's 739 pages not including the index, and I guarantee that if you read it from cover to cover and actually UNDERSTAND and remember it all, you'll be more knowledgeable about digital audio than ANY person who's EVER posted here, period... Steve
Cool.