Wolfgang Amadeus Mozart wrote over 600 pieces of music between his birth in 1756 and his death in 1791. Mozart composed his first piece of music at the tender age of four, and continued to write compositions right up to his death, and many of these pieces are considered to be the greatest works of their kind so it is important to have a clear system of identification. These are usually identified by their K or Kochel numbers, after Ludwig von Kochel who made the first full catalogue of Mozart's works in 1862. Experts who revised the catalogue include Paul von Waldersee (1905), Alfred Einstein (1937, 1958 and 1961) and Franz Giegling/Gerd Sievers/Alexander Weinmann who collaborated in 1964, 1865, and the most recent revision by Giegling/Sievers/Weinmann was in 1983. However Mozart's works are still universally known by their K (or Kv) numbers.
The original catalogue included a short snippet of the music (known as an incipit) at the beginning of each work, so that it could be identified. However since the time Kochel's catalogue was published many more works have been identified or reattributed, and the catalogue has undergone several revisions. Even so the Kochel numbers are the accepted way of identifying Mozart's works. He wrote many different symphonies, 27 piano concerti and 28 piano sonatas to take just three examples and it's really helpful to be able to talk about "Piano Sonata K330 in C Major instead of just "Sonata in C Major composed circa 1781-1783" and hope that your informant will know what you are talking about!.
The importance of Kochel's work in laying out the original catalogue and identifying Mozart's works in this way cannot be underestimated and provides scholars and musicians alike with considerable assistance when finding the music they want to play or study.
Some works are not usually identified by their K numbers although they do have them. Examples include the operas (Die Zauberflote is K 620) and some of the symphonies which have been given their own nicknames. The Linz symphony (Number 36 in C Major) is one example of this, but in cases where works have been given nicknames they are usually also known by their K numbers, which in this case is 425.
You can view the full list of Kochel numbers at Wikipedia.
The Kochel catalogue is a wonderful and very important tool without which the works of Wolfgang Amadeus Mozart would be very much more difficult to identify today.