Browser tries to resolve the name cnn.com into its ip address.
Browser TCP connects to cnn.com's ip address on the default HTTP port (80)
Browser sends a GET request to the server, asking for the / page
Browser says that it's trying to connect to "cnn.com" (cnn.com and bbc.com could be hosted on the same hosting company, with the same IP address)
Browser also says what's your browser, browser engine, browser version, operating system and the plug-ins that you have installed.
Server sends a header saying what's coming on your reply, the kind of data you're going to receive (in this case, HTML), and the size of the response if it's available.
Server closes the connection if there isn't any keep-alive instruction from the browser. Otherwise it will use this opened connection to ask for other things that might be needed (images within the page, for example.)
By the way, download and install Wireshark if you want to go deep and see what's really going on behind the curtains.