The problem is that people tend to assume that smaller files mean compression has happened, but not loss. This is not actually the case.
With a compressed data file, like a Windows 'ZIP' file format, the original data is all safe. Nothing is lost, it is just compressed using mathematical algorithms that allow some data to be stored as mathematical expressions instead of actual data. So when you 'unzip' the file, the original data is restored completely. It should be bit-for-bit identical to the original.
MP3 is not like ZIP. It is (as described by others above) as a 'lossy' format. It is designed to make audio files smaller in size like ZIP does, but it doesn't just compress the data; it also removes data based on an algorithm that was originally designed to not sacrifice 'too much' audible quality. It essentially 'throws away' information in order to save space. That information cannot be restored by any means once it is gone. An MP3 file is NOT identical to the original source, and it cannot be 'unzipped' or made back into a duplicate of the original file.
FLAC and WAV and other 'lossless' formats compress audio files without throwing away any data (if converting from digital to digital). Some quality may still be lost if the conversion is from an analog original source to digital storage, but this is a matter for a different discussion.
Therefore, whenever possible, save your music from CD in a lossless format. The resulting files will be larger than equivalent MP3 files, but they are functionally identical to the original (again, if the conversion was from digital to digital).
Once converted to a lossless format like FLAC or WAV, one can further convert files to MP3 as desired. The MP3 files can be useful for things like portable music devices. But don't discard your lossless files when you make MP3 files. The lossless formats will still be superior for any playback device that can properly handle them.
Hope this helps.