Hey sadboy,
I'm going into 1st year this year too, so can only tell you what I've picked up briefly from my older brothers and sisters. Someone on here will certainly add to or correct what I say, but I'll give you my thoughts now.
Basically to major in something, you need to make up a certain amount of "units" for this subject. I think across 3 years, if you play your cards right, you can major in 2 subjects. That said, you can also major in nothing if you don't have any consistency with your subjects.
"Breadths" are classes that aren't specific to your course, but are taken to increase the "breadth" of your studies and to make up your 300 units so you can get your degree. For instance, my brother was a slackass Science student and took Wine Tasting, Sports Coaching and African drumming as his breadths!
As far as "the whole system", take a look at the student handbook (google UniMelb Handbook) and it explains a lot
