Honest question, as I've never really understood the industry: where does this money come from and why? And where does the money go that acquisitions and IPOs earn them?
So A16Z raises commitments of 1.5B from all of these people who have a lot of money that they want to grow. Those people deploy their capital to VC, to Hedge/PE funds, to timber, to public markets, to bonds, etc.
A16Z aren't actually given a pile of cash though, instead A16Z does capital calls on an as-needed basis. Then A16Z deploys that capital to startups and other companies over the life of the fund (often ten years with some extensions).
Most venture funds operate on something like a "two and twenty model" meaning that every year they get 2% of the funds value for operating expenses. In A16Z they have a huge staff of designers, recruiters, BD experts, etc, that help their startups. The 2% goes toward things like that.
The 20% is carry, which is earned as a percentage of net income. So let's say that A16Z invests 5M in a company on a 10M pre-money valuation. A16Z owns 1/3 of the company. The company sells for $30M the next day to Facebook. A16Z now has $10M dollars. They take $2M of that for themselves and then they distribute back to the LPs the other $8M.
(This is lacking a lot of nuance like side funds, but I hope it's helpful).
One thing to like about a16z (full disclosure, I worked there over the summer), imho, is that by using this fee to scale their organization to help portfolio companies, they are far less out of alignment with LPs than most firms who have success with a smaller fund and go on to raise a larger one.
The old algorithm of do ok with a small fund, raise a huge one and live off the management fee is under threat -- 5x or die.
I'm pretty sure carry is profit (http://en.wikipedia.org/wiki/Carried_interest), so in your example A16Z would pocket $1M, not $2M (because the $5M A16Z invested needs to be repaid to the LPs first, and then A16Z gets 20% of the remaining $5M). Please correct me if I've misunderstood.
(Edit: I realised you usually go by Zac rather than Zach :)
When there is an exit--a sale of stock--most of the money goes back to these LPs. The money is (more or less) split like this: the LPs get their investment back first then, of the gain, 80% goes to the LPs and the rest goes to the company managing the venture fund to split up as it pleases (this last 20% is called the "carry".)