A camera lens collects light, focuses it, and projects an image into the camera body. The lens is round so the image that it projects into the camera body is also round. BUT... the camera sensor is rectangular. The sensor is located smack in the middle of the image circle being projected into the camera body by the lens.
If you had a "full frame" camera body, then the sensor measures 24x36mm or about 43mm diagonally. So the image circle being project in by the lens needs to be at least 43mm in diameter to cover the size of the sensor.
On a "crop frame" camera body, the sensor measures about 15x22mm (the original APS-C was slightly larger) or about 27mm diagonally.
When an "EF" lens is projecting an image into your camera body and that image is 43mm across, but YOUR camera records the central area of it which is 27mm across, that just means that some of the image is "spilling off" the sides of the sensor and not being recorded. Your camera does not actually know this, however... it has no idea that there is any part of the image that was spilling off the sides. The area that it records on the sensor is the whole image as far as your camera is concerned.
Canon makes another series called the "EF-S" series. These lenses take advantage of the fact that the camera sensor only needs an image circle with a 27mm diameter. The lenses are a bit smaller, lighter, and less expensive and yet they can STILL deliver quality just as good as the larger lenses. They simply don't bother to use lens elements large enough to create a 43mm image circle... why bother when the sensor couldn't record that part of the image anyway.
Canon makes an EF 50mm f/1.4 lens. Now suppose Canon _also_ made an EF-S 50mm f/1.4 lens (they don't... but suppose they did.) The "EF-S" version would be more compact. But when you switch between the two lenses on your 60D camera body, you would not notice ANY difference at all with respect to the size of the image or the angle of view. It's just that the "EF" lens is also capable of working on a full-frame body and if you used a full-frame body you'd see that the lens sees a larger area than you were previously aware.
Your TV screen is a different story and this has to do with aspect ratios.
The camera sensor has a 2 X 3 aspect ratio. That means for every 1mm tall, it's 1.5mm wide. When I gave you the 15x22 dimensions, I rounded the numbers. The actual numbers are 14.9 x 22.3.
A TV, on the other hand, used to be 3 X 4. That means that for every 1mm tall, it's only 1.33mm wide. Modern TV's may be 16 X 9.
Unless the dimensions of the TV screen are an exact ratio for the dimensions of the camera image, then one of two things must happen: (1) to fit the "whole" image on the screen, it has to leave black space either above & below the image OR left & right of the image (depending on the aspect ratio of the TV) , or (2) it has to "crop off" some part of the camera image in order to completely fill the TV screen.
You will probably discover a similar issue when you want to have images printed. If the dimensions of the print exactly match the 2x3 aspect ratio of the camera, then no problem. But if the image does NOT exactly match the dimensions of the camera (say you want an 8x10 print... which works out to a 4x5 aspect ratio) you'll notice that part of the image has to be cropped to fit the frame.