Lossless audio refers to an audio format that completely preserves all of the original recording data without loss in encoding. This allows perfect reproduction of the original audio signal when played.
Formats such as WAV, AIFF, and FLAC are some lossless audio formats.
Lossless splits into two kinds that are often confused. FLAC and ALAC are compressed lossless: the file is packed down to roughly half its original size, then unpacked perfectly on playback, so nothing is lost. WAV and AIFF are uncompressed: the audio data is simply stored as it is. Both reproduce the recording exactly, they just differ in file size, so a FLAC and a WAV of the same master sound identical.
Whether it is worth the space depends on what you are doing. For archiving your library, lossless is clearly better because it gives you a clean source to convert from later, however formats change. For playing out, the difference between a true 320 kbps file and lossless is very difficult to hear through a club sound system in a room full of moving people. Take lossless when it costs nothing extra, but gain staging and the quality of the original master affect what the floor hears far more than this choice does.
See Also
Lossy Audio, file format, and FLAC