Ripping is the process of extracting audio from a CD and storing the music files on your computer or NAS. There are some media servers that do this automatically, but also a lot of people use their computer for this task.
Today most people extract their music to a lossless format like FLAC. There is software that specialises in providing the best quality extraction to make the most of the music. The extraction process, like playing a CD, can read errors in the music data. When playing a CD this results in clicks and pops in the music. Because the ripping software does not need to read the music as it is being played it can try and do a better job than a CD player. It does this by detecting errors and attempting to re-read the bad data. Modern drives are very fast at reading data, so while the CD ripping process may require multiple reads, it still normally proceeds much faster than playing a track.
Many CD ripping applications participate in a database called AccurateRIP. How this works is that the AccurateRIP server stores data from other peoples extraction of CD data, and compares this to your extraction. If the data is the same then we can be confident that the rip is error free. If there is no data available or if the checks don't match then we may have a problem. In this case the CD ripping software may take extra steps such as extracting the data again until it gets consistent results.
Once the data has been extracted from CD it must be encoded in to a music file. In the past most people used MP3 for this as the files were compact. MP3 uses various tricks to make the file smaller while trying to maintain as much audio quality as possible. It is an example of a 'lossy' format, some information is lost in the compression.
With todays low cost of storage most people use lossless formats, such as FLAC. The data is still compressed to save space, but when uncompressed it is identical to the original.