Blockchain.info doesn't have any fees of their own. The most common bitcoin protocol in the bitcoin network has rules that can require a fee to the "miners" that build the blockchain. Blockchain.info sent you here, because your question isn't about blockchain.info, it is about how bitcoin is designed to work right now.
Any transaction that is more than 10,000 bytes in size (from an excessive number of inputs), or that uses inputs that are very small (less than 0.01 BTC), or that uses very new inputs, will generally require a fee of 0.0005 BTC per kilobyte. Without the fee, many of the bitcoin nodes on the network will refuse to relay your transaction, and some miners will refuse to include the transaction in the blocks they mine.
That would be a nice one liner for Blockchain to post on their buy/sell page then. Making their users aware of this. I guess they expect every to know everything about everything. Doesn't matter now, I stopped using their service and went back to old reliable. My local wallet.