As odd as it might seem to non-technical people, it does really make a difference what cable you use to connect your PS3 to your TV. The cable helps to define what type of signal your TV receives. Think of it as listening to your CDs on a tinny little $5 plastic speaker, vs listening to your CDs on large, high quality multi-speaker surround sound.
The options for video (TV) output cable connection for your PlayStation 3 are composite and HDMI. Composite is the old style VCR type of cable where there is red and white to carry the right and left stereo signals, and a yellow plug to carry the video. If you use that set of plugs, that is ONLY regular TV quality. That is the maximum level of quality it can carry.
All PS3s ship with this composite cable as their default cable.
To get a higher level of video quality from your PS3, you need to buy a separate cable - a HDMI cable. This carries high definition video plus audio, all in one rectangular-jack cable. This is sending in essence a bunch of zeroes and ones all in a stream. The transfer rate, if you're curious, is 5 gigabit per second. In comparison, moving a high def movie signal only takes up 2.2 gigabits per second.
With analog cables, i.e. the older cables that sent sort of a "sound wave" of signal, it really mattered how high quality the cable itself was. Using gold plated connectors, shielded cables and so on could really affect the quality of that sound wave as it travelled from its source to its destination.
With new digital cables, this shielding really doesn't matter that much. It's moving 1s and 0s. It's like a wireless network connection. You don't worry about "walking between" that signal. It's ones and zeros moving, which is simple to move around.
So that being said, your main concern when buying a HDMI cable is that it's long enough to suit your needs. You don't have to buy multi hundreds of dollars for a high end HDMI cable because it's "better". You can buy a standard HDMI cable and get the exact same level of quality.
Note that there is NO reason to get something "specific for a PS3" here. Both ends of a HDMI cable is a HDMI jack. There's nothing at all PS3 specific in this cable. You can get any HDMI cable in the world and it will work fine for your PS3 or for any other HDMI application you might use.
If you really want to go solely with Sony products, feel free to pay more for the Sony version of the HDMI cable, which is made by Monster. Monster is a well known name in high end cables. However, if you want to save some money, there are many other options out there for you to choose from.
Buy the Sony HDMI Cable from Amazon.com