In the "my positions" table on a page for a given market, there are numbers for net position and quantity. What do these mean, and what's the difference? In the screenshot below, I have a position open as well as a buy and a sell order.
The Yes/No markets are in fact a bit confusing in Augur. The key point to understand is that there are not only YES shares but an equal number of NO shares. Unfortunately, the latter seem to be invisible in the UI.
In a new market there are no shares at all. Imagine I create the first order and offer 0.7 ETH for a YES share. You decide to fill the order which you can do even if you don't have any YES shares yourself yet. You basically short the YES outcome and this is implicitly done through the creation of the NO share. Effectively, you bid 0.3 ETH for a NO share (that's also what you pay when you fill my order) and each of us gets one share of the newly created YES/NO pair and 1 ETH is locked up in the Augur smart contract.
You just don't see the NO share in the UI but you see the "net position" of -1 YES shares.
Now imagine you continue to trade in this market and you see a sell order for YES shares at 0.6 ETH. Actually, you can't easily tell if someone is selling YES shares or buying NO shares, so let's rather say "someone wants to go long the YES shares at 0.6 ETH". Let's assume the quantity is 1 share and you take the order because you can realize a profit (you went short at 0.7 ETH and now you buy back at 0.6 ETH). If the creator of the order was buying NO shares, your NO shares are actually transferred. However, if your counterpart was selling YES shares instead, the YES and NO shares disappear in the process. This is an implicit settlement of a complete set and incurs settlement fees.
It can happen that you hold YES and NO shares at the same time, for instance if your NO shares are locked in an order and you buy some YES shares. So this is when the "net quantity" or "net position" is relevant. The Augur UI allows you to settle such complementary shares. To be honest, I'm not exactly sure about the quantity column. It also shows 0 for all of my positions.