FLAC stands for Free Lossless Audio Codec, an audio format similar to MP3, but lossless, meaning that audio is compressed in FLAC without any loss in quality. This is similar to how Zip works, except with FLAC you will get much better compression because it is designed specifically for audio, and you can play back compressed FLAC files in your favorite player (or your car or home stereo, see supported devices) just like you would an MP3 file.
FLAC stands out as the fastest and most widely supported lossless audio codec, and the only one that at once is non-proprietary, is unencumbered by patents, has an open-source reference implementation, has a well documented format and API, and has several other independent implementations.
FLAC is easily playable on your computer using Foobar, DB Poweramp (with FLAC plug-in), MediaMonkey, or Winamp (with the FLAC plug-in). Or you can always use VLC Player - it plays everything!
You can play FLAC files on portable equipment, but most of them are not manufactured anymore. You should be able to find them used on the internet or your local electronics shop. I use a Rio Karma with a flash drive replacing the original hard drive. It holds about 20 GB, which is about 40 CDs.
The FLAC community uses EAC to rip CDs. It's important to have your CD/DVD player have the proper offset configured. It is also important to include the LOG file. That helps other people know the FLAC files are authentic. There are still some FLAC files floating around the internet that are really re-encodes from lossy sources. It would also be helpful to include the CUE file. EAC can easily burn a CDr with the source FLAC files and the CUE file.
A useful utility to have is Trader's Little Helper. This utility can encode and decode lots of different lossless audio files (e.g. ape, flac, mkw, or shn files). It will also test files for MP3 source. It is freeware. If you need to decode the FLAC files down to MP3, this is the easiest program to use.