Creating the Illusion of movement has been the fascination of many throughout history. Early examples of this can be found in cave drawings and on pieces of pottery. However these really can't be considered animation in the truest sense of the word, even though the artists were trying to show some form of motion.
The first flip books appeared in the 19th century and were a little closer to what we would consider animation in today's world. These books consisted of drawing that would show the illusion of some sort of movement, when the pages were flipped quickly and in a coordinated manner.
True animation cannot be considered being born until the advent of the motion picture or what is known as cinematography. With the use of the motion picture animators could produce high quality animation such as stop motion and animated cartoons.
Animated cartoons became very popular in the early 20th century. They were often shown before full length feature films and were usually only six or seven minutes long. These types of animated films where know as cel animations and each frame had to be hand drawn. Each cel or drawing had a slight change in the characters position, which gave the illusion of motion. The completed cels where photographed one by one against a background picture. Warner Brothers and Walt Disney animation studios produced many high quality animation shorts of this nature during the 1940's and 1950's.
Today animated cartoons re no longer produced using this method. Computers and 3D animation software has taken over. There are many types of computer animation. They all have one thing in common, they produce digital imagines on a computer and take much less type to produce than hand drawn cels. Of course you need to known how to proficiently use the software and have access to it.