Tip Opening: This is the distance from the tip of the reed to the tip of the mouthpiece (when a reed is in place). The wider the tip opening (or higher the number), the brighter the sound (think jazzy). It is also harder to play (reed has to travel farther to vibrate), but it can help you play louder without the reed choking.
Facing Lengths: The facing is the length of the reed that is not touching the mouthpiece (again, when it’s in place). The longer the facing, the higher the amount of the reed is vibrating when you play. This means it may require more muscle to play with a long facing, but it will produce a fuller sound (better tone quality).
Chamber Sizes: The chamber size the how hollow the mouthpiece is. The wider (or hollower) the chamber size, the warmer and fuller the sound – but it can also sound dull if it is too wide. The narrower, the brighter and crisper.
The reason there is so much on mouthpiece specifications is because it is the most important part of your instrument (aside from the reed itself). I’ve seen many people make huge improvements simply by investing in a quality mouthpiece. Small changes to each of these variables can help you attain the particular tone you’re looking for.