Decentralization is an organizational system opposite to centralization. It involves taking the pieces required to operate a system and spreading them out for the purpose of either security or efficiency. A good example of decentralization is a monarchy versus a democracy. In a monarchy the decision making power for the whole kingdom is given to one person. A democracy is an attempt to decentralize governance by taking the governing power out of the hands of one and into the hands of many.
An example of a decentralized application for a computer is the torrent. A torrent is an alternative way to download a file. Rather than receiving it in one piece from a database, they receive it in little pieces from hundreds or thousands of other computers who have already downloaded the file and are uploading pieces of it from their home computers. Torrenting software re-assembles the file pieces for the downloader and delivers it to the user quickly and in one piece. Some gaming companies use torrents for game releases so that many users can download large game files quickly and simultaneously.