On the Receive screen in the IOTA Wallet there's a button labeled "Attach to Tangle":
I thought attaching to tangle only applies to transactions, not addresses. What does this button do?
This button will create a transaction that will send 0 iota to the newly created address.
That way, the address appears on tangle explorers (and senders might use this as an indication that the address is indeed correct).
Furthermore, if you create a new address and attach it, and pass it to somebody to pay you, and you need another address before that other person actually pays you, your wallet will know that it already used that address and will create a new one instead (for the next person who wants to pay you).
Otherwise it could happen that the first person would pay you after you used the money you got from the second person, and therefore you'd have to reuse an address to get the first person's money off the address.
For sending iota, it is not required to "attach" the address first; the iota will appear anyway and the address will get "attached" by the transaction that sends the iota automatically (so you do not need to attach an address for a paper wallet, for example).
You attach a 0-value-transaction with a newly generated address to the Tangle. (do the POW, tip selection, ...)
It could be used as a precaution e.g. a wallet only allows you to send IOTAs to addresses that are already attached to the Tangle so that you cannot mistype and send to an address without an owner.
But the light wallet has not implemented that at the moment. You will still receive your IOTA if someone sends them to an address that's not attached to the Tangle and you are able to send IOTAs to addresses that are not attached to the Tangle.
It also helps the network because everytime you attach a transaction to the Tangle, you verify 2 others.
When hitting the "Attach to Tangle" Button, the wallet will do the required proof of work and broadcast the "recieve adress" in the network. With that the wallet will remember which adresse's where already used. And when switching to full node, you can see the adresse's balance.
So it's not mendatory to attach the adress to the tangle to recieve IOTA's.