Morse code was developed in the early 1800's for the first land-line telegraph systems, as a means of sending messages via electrical impulses over long distances. Morse Code is named after it's inventor, Samuel F B Morse. A modified version of that code is in use today by ham radio operators world-wide. This version is commonly known as "International Morse" (or sometimes, as "Continental Morse").
In the beginning days of radio, no one understood how to construct equipment capable of sending and receiving signals using voice, so Morse code was the only means available. Morse code remains the simplest and most efficient way known to send messages via radio. It is easier to construct a Morse code transmitter and receiver than any other communications apparatus, and messages can be sent with very low transmitted power. Morse code signals (also known as CW, for Continuous Wave) penetrate interference, both natural and man-made, better than most of the more complex schemes.
It is entirely possible to construct a working Amateur Radio set for only a few tens of dollars, including antenna and accessories, and (using Morse code) use it to contact stations thousands of miles away. For a personal example, click here. In fact, an entire group of Amateur Radio enthusiasts specialize in building and using very simple, low powered stations (known as QRP, in ham radio parlance). There are thousands of QRP (low power) enthusiasts around the world. The relative power efficiency of CW is of particular benefit to operators who use simple low-powered stations, which is likely to be the case for operators from developing nations.
One of the areas where CW is clearly superior to most other modes is bandwidth efficiency. The only other mode that can compete with this remarkable efficiency is PSK-31. Bandwidth efficiency is especially important in the amateur service given our limited allocation.
We all know what SOS stands for. In the morse code world there are many other such abbreviations. These make it possible for operators who do not speak the same language to communicate at least basic information. This means that proficiency in English is not a requirement for successfully communicating worldwide using CW, which is an obvious benefit in our attempts to facilitate good will around the world.
Because Morse code equipment is so easy to construct and operate, and because it has the capability to get messages through when other modes fail, and because it is universally understood by operators in all countries, the governing bodies that make the international rules for Amateur radio have wisely decided that Morse code should be a continuing part of the Amateur radio system.
As of 2007, getting an Amateur Radio license no longer requires passing a code test. Many people now enter the ranks of Amateur Radio without learning Morse code, only to pick it up later and enjoy its many benefits.