As mentioned, the main advantage of HDMI 1.3 is that it allows you to transfer HD audio soundtracks as a raw bitstream to an AV receiver. If your player supports this feature and you'd like to take advantage of it, you'll need to track down a receiver that not only provides HDMI 1.3 ‘repeater' inputs but also decodes some or all of the HD audio formats - Dolby True HD, DTS HD Master Audio, Dolby Digital Plus and DTS HD. With your player rigged up to the receiver's HDMI input, the HD audio bitstream is passed to the receiver to be decoded, while the hi-def video is passed through the receiver's HDMI output to your display.
Receivers that decode all or even some of the HD audio formats aren't cheap, but the good news is that you don't necessarily need one with built-in decoding to experience these new-fangled formats. You don't even need one with HDMI 1.3 inputs, and here's why.
Most Blu-ray players can decode HD audio soundtracks internally and output them as uncompressed multichannel PCM, which is supported by all versions of HDMI. You can therefore enjoy higher-bitrate audio soundtracks on players with HDMI outputs earlier than v1.3 without any loss of quality - provided that your receiver has an HDMI input of course.
If it doesn't, then you can use the player's 5.1 or 7.1-channel outputs to transfer the decoded audio signals in analogue form. This is good news for owners of older amps who don't want to upgrade, although it does mean you have to endure the hassle of rigging up a rat's nest of analogue cables as opposed to a single digital cable.
If this all sounds like one big headache, then the simplest way of getting all the relevant decoding and connections is to pick up an all-in-one Blu-ray system, such as the Panasonic SC-BT100, or the Samsung HT-BD2R.