MP3 is short for MPEG-1 Audio Layer 3, according to file-extensions.org. It is one of the most popular and commonly used formats, especially among music consumers and home computer users. MP3 is "a patented digital audio encoding format using a form of lossy data compression..." Lossy compression results in loss of audio quality in digital recordings. MP3 file format is used "for consumer audio storage...[and is]...a de facto standard of digital audio compression for the transfer and playback of music on digital audio players." It is the best known music file format.
WAV is the file extension used to store PCM files, the most widely used uncompressed audio file format. On a Mac, the file extension for a PCM file is AIFF. According to file-extensions.org, "WAV and AIFF are flexible file formats designed to store more or less any combination of sampling rates or bitrates." Thus, these formats are most often used "for storing and archiving the original recording." Unfortunately for home computer users, high-quality PCM-format music files may be as large as 10 MB per minute. Therefore, compressed formats are more practical for the home user.
FLAC stands for Free Lossless Audio Codec. Like MP3, FLAC is a compressed format. On the upside, FLAC is "lossless, meaning that the audio information is compressed in FLAC file without any loss in its audio quality," according to file-extensions.org. This means it will give you better sound quality than the typical MP3 file. On the downside, FLAC will "require more processing for the same time recorded..." than MP3. If you want better audio quality than MP3 in a smaller file than WAV, FLAC is a good choice.