When the recording process has finished, there should be a multitrack version of a song or group of songs that is played to the best of the performer's ability, is in time, is in tune and contains no mistakes. This is where the mixing process starts. The mix is the time when the levels of the individual elements of the recording are balanced, equalised, processed and effected in order to create a more defined, clean and interesting sound. Each instrument should be clearly defined in it's own space and not be conflicting with other sounds. As an example of the dramatic effect that mixing can have on a song, listen to the example below of an unmixed track. This sample is made up of the raw sounds captured at the tracking stage and is totally un-effected by any processing.
Now have a listen to a version of the same track which has been mixed. Hopefully you should be able to notice a vast improvement in the overall sound, the overall power and the balance and clarity of the individual instruments.
The example outlined in the first paragraph of receiving a perfect version of the multitrack recording for mixing, unfortunately doesn't always happen and it is often left to the mix engineer to correct mistakes that should have been fixed in the recording process. While the 'fix it in the mix' attitude can sometimes work well, it often takes more time and effort for the engineer than it would have done to have had the performer play the part again correctly. While it is true that certain sounds can be replaced (drums for example) and guitars can be re-amped etc... these changes have to be made by the engineer, not the artist and as such could impact the way the music is performed.