Common lossless files:
Apple Lossless
FLAC (Free Lossless Audio Codec)
Monkey's Audio
Shorten
etc.
Common lossy files:
MP3
AAC
Ogg Vorbis
Conversion to a lossless format means that there will be no loss in quality. You can rip a CD to lossless and be assured that you will never, ever be able to detect any quality difference. You can convert that lossless file into any other lossless file and maintain the quality. You could, similarly, convert an MP3 or another lossy file into a lossless file and maintain the same quality of that original MP3 file, but there's no real use for that.
Conversion from a CD or a lossless file to a lossy format means that you will lose some data. Lossy formats are designed to throw away data in a manner that your ear will hopefully not know the difference. Thus, while all lossy formats can be thought of as objectively "lesser quality," the key question is whether or not you can perceive that loss in quality. If you convert a lossy format to another lossy format (AAC to MP3, for example) the loss in data is compounded, making it much more likely that you will notice distasteful quality loss. Sort of like repeatedly making a photocopy of a photocopy.