Here's my attempt at some simplified explanations. It's not as short as I would like it to be, but I think it does a fairly good job of getting the idea across, especially to people with minimal technical knowledge. Let me know if anything is inaccurate or you think there's a better way of explaining things:
DAC stands for Distributed Autonomous Corporation. The basic idea is that some service offered by normal corporations, run by humans, can be performed using software on computers. People who want to work for a particular DAC can download this software, and then run it on their computer. The more computing power that people give to the DAC, the more reliably the DAC can perform the service it offers for its customers. If somebody wants to buy the services of a particular DAC, they can pay the DAC directly for the service using some digital currency, such as Bitcoin or shares in the DAC, and then they receive the service from the DAC, and their payment is distributed to the people who ran the software for the DAC, corresponding to the computing power they gave to the DAC.
Every DAC that Invictus Innovations plans on creating will have shares. The purpose of these shares is two-fold: they determine who gets to receive the payments given to a particular DAC (just like a major corporation would divide its profits among its shareholders), and they also function as a form of payment to the DAC. In other words, the DACs that Invictus Innovations will release will take shares in themselves as payment, and then re-distribute those shares among the remaining shareholders. Protoshares are a digital currency that turns into shares in all DACs created by Invictus Innovations. They are “mined” by running special mining software on your computer, and each time a DAC is released by Invictus Innovations, you will get one share in that DAC for every Protoshare you own. One advantage to using Protoshares to create the shares for the DACs before their release is that Invictus Innovations is able to determine valuable people expect shares in a particular DAC to be, since people know that every Protoshare they buy will effectively buy them a share in future DACs. In order to tell how much an individual DAC is valued by the market, Invictus Innovations will simply fork the current Protoshares, and say that the particular fork corresponds to a particular DAC. (Forking is essentially cloning something so that you can manipulate /change the clone, without affecting the original.)
Now, let’s take an upcoming DAC, and explain what problem it fixes, and how it solves that problem:
Problems it addresses:
Let’s say I want to trade digital currencies. In order to do it I need to log onto an online exchange, and then give them my email & password. Then, I send them my bitcoins, and start to trade. There are many things that could go wrong here: 1) they might sell my personal information, 2) they might take my coins and vanish, 3) If hackers compromise the exchange I could lose my bitcoins, 4) if I want to trade multiple currencies that aren’t all offered on one exchange, it’s very hard to manage all the different accounts and transferring the funds between them.
How Bitshares fixes this problem:
1) I don’t give my personal info to anyone. I simply download the client, and then I can start trading, the only account I need is the Bitshares address that my computer can generate automatically
2) As long as there are still people mining on the Bitshares blockchain, the DAC will continue to live. Also, Bitshares never actually takes your funds, it simply allows two people to trade with each other, knowing that the DAC will ensure that both sides send their funds to each other at the same time, thus your funds never actually leave your control, they’re simply traded for different funds (i.e., Bitshares for BitUSD
3) There is no centralized server for hackers to attack. In order for them to actually steal your funds they would have to derive your private key (Which basically means doing a bunch of math that would take centuries to on a supercomputer, so you’re safe) and submit a false transaction using that key. Then they could steal your funds (remember, this is only a problem if they have access to a supercomputer more powerful than every supercomputer currently know). They could also try to block any transactions you submit by performing a 51% attack, where they gain 51% of the computing power in the DAC, and then do the work of verifying only some transactions so quickly that everyone else that’s trying to do work is unable to keep up with them, so only the people performing the 51% attack decide which transactions the DAC performs. Remember, in order to do this they need more computing power than everyone else combined, which is a LOT.
4) No one Bitshares blockchain will cover every asset that you may want to trade. However, all Bitshares blockchains will trade the original Bitshares, which will make the exchange of funds between them much simpler.
I think this does an OK job of explaining things, I'd be happy to answer any questions you still have.