There are a few different ways to connect devices to your home theater system to provide full surround sound. The most popular method is HDMI, a simple cable that carries both video and audio. The second most popular is an optical connection (also known as "TOSLink" and "S/PDIF"), which only carries the audio data and requires a separate connection for video, like component or composite cables. The other method is analog, which uses a different cable for each channel of sound coming from the device. Simply from their descriptions, it's fairly self-evident which is the superior connection--HDMI is more popular because it's an all-in-one digital solution.
The newest HDMI standard, 1.4, adds another useful feature to the cable that other connections lack. HDMI 1.4-compliant devices can use "Audio Return Channel," where a cable that sends a video signal upstream can receive audio downstream. With the increasing popularity of HDTVs that can access web-based content, this means the same cable that pipes video from the receiver to the HDTV can pull the audio signal from the HDTV's web-based features down to the receiver. It removes the need for a second, dedicated cable to carry audio data from the HDTV to the receiver.
The analog connection has the same benefit as vinyl to audiophiles: the purity of the sound. The sound isn't encoded in any way; the device, like an SACD player or a vinyl turntable, decodes the audio from the media itself (whether by needle or by laser), and sends that very signal straight to the receiver, the preamp, or the amp, and then to the speakers themselves.
It's a distinction that casual users rarely make, but it's the exact same reasoning that causes many purists to zealously guard their vinyl LPs and scoff at CDs, DVDs, and even lossless music downloads. It's more "natural." There's no electronic transmutation of data; the sound that the player picks up is the same sound that goes to the amp and the speaker.
If you're just setting up your home theater now, or you're considering upgrading your receiver or Blu-ray Disc player, use HDMI. It's convenient, simple, and easy to set up. If you're an audiophile and you want to get the most out of your collection of vintage albums, then you're probably already using an analog stereo connection right now. If you don't want to switch out your years-old DVD player and don't care about lossless audio, you have to make the choice between surround sound via an optical cable or stereo sound via analog cables.