Where does Coinbase buy coins from? When we buy coins from Coinbase, where do they get the coins from?
Coinbase is built on top of Bitstamp. They may work with other exchanges now, but they are (and used to be) very tightly coupled with Bitstamp. 

There was an exploit where someone discovered that Coinbase's price was set to the last sale price on Bitstamp.  Basically, this person would sell a small amount of Bitcoin for much lower than market value on Bitstamp.  Coinbases price would match that, where he'd buy again. 

Coinbase does operate their own reserves as well, which (as others have pointed out) are used when Coinbase customers buy and sell within the site.  Their prices are set using a weighted average of multiple exchanges.