Back in the stone age when we all used film, 35mm became the gold standard film size. When we switched over to digital, there was no film to be used. On most DSLR cameras, the digital imaging sensor, which replaces film, is significantly smaller than 35mm film. In 2002, the first sensor that equaled the size of 35mm film was produced.
Canon was the first mainstream camera manufacturer to produce a DSLR camera with a sensor the size of 35mm film. I can just imagine how the meeting went when the executives at the Canon marketing department sat down and tried to think of a way to make their new DSLR seem ultra-incredible and make everyone else’s camera seem like it was half a camera. They accomplished this task by calling their 35mm equivalent sensor a “Full frame” DSLR camera, and decided to call all other DSLR cameras “Crop frame” cameras.”……………..more including pros and cons of the various options
Here are some pictures that might help you understand the size ratios of the various sensor sizes
This explanation has images taken from full frame and crop sensor cameras from the same location using the same focal length of lens, it is a useful read also....here
In the image above I took two pictures from the exact same location with a 30D and a 5D. I used the same lens (Canon 24-105 f/4L IS) on both photos at a focal length of 24mm. By overlaying 100% size images on top of each other you can see how much more of the scene is captured by the 5D’s full-frame sensor (the color 30D image is on top of the black & white 5D image).
Here is another example of the two images Crop Sensor
Full Frame Sensor