2-way pegging means that value may be transferred at a pegged (fixed) rate in either direction.
This special form output is a script which is able to understand an embedded proof-of-spend from another chain, which validates the accounting rules (you need to spend X bitcoins to claim X sidecoins, and vice versa), and which makes sure that claimed coins go to the indicated recipient.
this question related to the red-marked quote:
What happens if I moved a BTC to a side chain to be used with a financial instruments such as options or even betting
and GAINED an equivalent value to what I moved out. I now have 2 sidecoins but previously moved only 1BTC. can I go 1-way with one of them?
Yes, because the 1BTC that you gained through trading had to be originally moved into the sidechain as well, and it can be redeemed in the same way.
Where did this gain, this additional sidecoin, come from?
Who knows? Trading? Betting? SatoshiSidecoinDice? Either way, that coin didn't come from nowhere. It came from someone who moved it into the sidechain from the mainchain.
So is it the case that at any time, anyone can move any amount of BTC that they control into any sidechain?
EDIT: What I am getting at is whether there are limits to the number of units on a particular sidechain. One does not need to find a "seller" or "redeemer" of sidecoins to make a BTC-sidecoin trade, since the sidecoin is not truly a separate unit of currency, so one is not really trading into it, correct?
(Thank you all for your patience and generosity in responding to my questions. I assume others trying to learn, too. I'm trying to piece things together from here and the two reddit threads.)