Lossy audio is audio that has been compressed using a method that diminishes the audio quality. Lossless audio is audio that has been compressed but has not lost any quality in the process.
Audio type examples: Some of the most common file lossless formats include FLAC and ALAC. MP3 is definitely the most well known lossy format
Normalization is different than compression because although they both affect volume, normalization adjusts the overall volume to a specific level (like making the loudest part 0dB), whereas compression reduces the dynamic range (the difference between loud and quiet parts) by squashing the peaks.