A FLAC file is an audio file compressed in the Free Lossless Audio Codec (FLAC) format and is noted by its file extension: .flac. It's very similar to the more readily recognizable MP3 file but is compressed to a smaller file size without any loss of quality or any original audio data, thus making it "lossless", a phrase you'll see often throughout the article.
The ALAC file extension is a data format associated with Apple Lossless Audio Codec (ALAC) and is noted by its file extension of .alac. These file types were developed by Apple, specifically to be used by iOS and therefore the iTunes platform. They utilize an M4A format and, similarly to FLAC files, they're in a lossless compressed format, meaning they aren't losing any quality or original audio data simply by being compressed.