Easy explanation of the declining steps of quality:
Music company has the original mix which was hopefully recorded decently and stored higher than CD's 44.1KHz 16bit, either in analogue or higher rated digital.
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Mix is 'mastered' onto CD, which is 44KHz 16bit. In modern times this process usually also involves lots of added compression which ruins the original dynamics (range of volume and also overall musical timbres when instruments are compressed together).
Mix is also often mastered onto vinyl which can't handle the modern compression (the indents in the plastic become too large and the head of the turntable has trouble remaining inside them) and therefore turns out to have better overall quality than compressed CDs.
Other audiophile digital formats exist such as DVD-A and SACD which have higher digital rates than CDs and generally are geared at a market who don't like modern compression.
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People who own the CD can compress the 44KHz 16bit digital representation into various formats which involves reducing the file sizes. Some compression (lossless) is like a zip archive, the archive shrinks the original contents, though when decompressed the original contents remain unaltered, other compression (lossy) intentionally strips the audio of as much it can trying to preserve the original quality, though the original accurately defined representation of the audio is no longer present. Newer lossy codecs, ogg speex aac wma, are more clever than the older mp3 at discarding less important parts of the sound/representing the compressed sound more efficiently. The smaller you go, the more of the original accurate definition is thrown away.
Vinyl owners can convert to digital, though often choose higher digital rates than CD because vinyl is capable of greater dynamics. They also have the choice of lossless or lossy.
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People can choose to compress further. If their original file is lossless, then they can convert between other lossless formats retaining the original quality or they can convert to a lossy codec, providing the same results as straight from CD to lossy.
If their original file is lossy encoded, then this file which has been reduced in size (as much as possible) and quality (as little as possible) by throwing away information not considered important according to one efficient method (or codec) is then put through another method which has its own rules for throwing away information. This results in a jumble of lacking data which inevitably degrades quality.
Sorry, that was more drawn out than I intended it to be