2-way pegging means that value may be transferred at a pegged (fixed) rate in either direction. The "2-way" is in contrast to one-way pegging, which is for example how Counterparty was issued. Unlike proof-of-burn, 2-way pegging involves sending coins to a special form of output which identifies the destination chain and recipient on the other side. At this stage it is similar to proof-of-burn: you have provably made the currency unspendable to you, and in doing so you gain the right to claim an equal number of coins at the destination side chain.
What's new is the return peg: to move those side chain coins back onto bitcoin, you perform the same operation again. First you send the side-chain coins to a special output naming the bitcoin chain and yourself as recipient. On the bitcoin side you take one of those previous burn-like outputs which sent coins into the side chain, and present your proof of having "burnt" sidecoins in order to claim an equal number of real bitcoins.
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 sortof-is and sortof-isn't fixed exchange rates. If you are coming from an economic background you know the problems of fixed exchange rates, but those problems don't really apply here. The problem with a fixed exchange rate over national currencies is that the two are not in fact equivalent -- you have two issuers that are separately backing each currency. In the case of 2-way pegging however, the two currencies are equivalent. You only ever get sidecoins by making bitcoins inaccessible, and vice versa. It isn't about fixing exchange rates between two currencies, rather it is about using the same exact currency on two different networks: sidecoins are bitcoins, and bitcoins are sidecoins.
Regarding innovation, monetary reward from speculative asset issuance is a failed model. Any innovation that occurs could be cloned on a side chain using bitcoins, freicoins, or some other already issued coin as the native currency. In a free market there is absolutely no reason to prefer the non-pegged alternative.
Not to side-track the discussion regarding two-way pegs - but.., Why do you think Freicoins (which has an 80% premine) should be a non-speculative standard that makes sense to use (despite the fact that the functionality is not yet implemented), where as Counterparty (which has better dispersed distribution than bitcoin btw) ought to be considered a failed model?