iTunes is a multimedia software from Apple which organizes and plays audio and video. Part of its programming is to organize your files into a library from which you can play music, movies, and TV shows. There are a number of options for how you can organize your library. Consolidation is one such option.
When you install iTunes, you will have the option to add music and video files from your computer or network to iTunes. By doing so, you will be creating a "library" that your iTunes application can use to locate your files for playback.
Your iTunes library is a set of commands that the application uses to find where the song or video that you want to use is located. The library is thus a list of references to locations on either your hard drive or another computer (if you are part of a local network). The files are not stored in iTunes itself.
Music and video files
Whether you are creating an iTunes library from one computer or various computers in a network, you likely do not have all of your music and video files in one location. Whether you have them organized in multiple folders in several locations or if you simply have a folder for music and videos, the files themselves are not located in the same folder.
Because of this, as you play audio or video through iTunes, each file you choose (or your computer chooses if you are shuffling) will have to have iTunes locate the file through its library to the location of the file wherever it is stored.
Consolidating your library
If you choose to consolidate your iTunes library, the result will be that you will create copies of all of the files in your library into a single folder (usually "iTunes music") on the hard drive of the computer from which you are running iTunes. It leaves the file in its original location as well.
The result is that you will have two copies of your files in your iTunes library; one copy in its original location, and one in your "iTunes music" folder.
Of course, you do have the option, at this point, to delete the original files and only keep the newly created copies in your iTunes library. This would make sense if you are only consolidating music and video from one computer, but may not make as much sense if you are copying music from another computer on your network, as that computer will not have access to the file any longer.
Advantages and Disadvantages
The advantage of this is twofold. One, it makes it easier to locate your music or video for playback because the files are all consolidated into one location. The other advantage is that if you either delete the original file or folder that contains the files in your library (or if you lose connection to the networked computers that contains the original files) you will still be able to play the files you want to.
The disadvantage to consolidating only becomes a problem when you have limited storage space. Having multiple copies of the same file may take up more space than is necessary, and if hard drive space is limited, this may become an issue. If you only need to keep your music and video files in one location, having the duplicates may be excessive and thus consolidating may or may not be a good solution for you. Deleting the original files after consolidating or simply moving all music or video to one or two files may be a better solution in some cases.