Imagine looking at the wall opposite to the TV. Would the TV project a sharp image on that wall? Or even a blurry one? No. The wall would just be quite evenly lit by the light coming from the TV. If you held a piece of photographic paper in front of the wall, it wouldn't make any difference.
This is because the light from the television is not directional. Each pixel is like a miniature light bulb that sends light to all directions in front of the TV. Thus, if you think of any single point on the wall (or on the film!), it is hit by some light emitted by every point on the TV, basically receiving the average of the colors in the picture shown.
Now, what we would like to do is to somehow force the light from one point on the TV to only illuminate the corresponding point on the wall. The most elementary way of ensuring this would be to hold a large piece of cardboard in the middle of the room, with a tiny hole in the center. What would happen then? The cardboard would block almost all the light from hitting the wall, but for each point in the TV picture, a tiny patch of the wall would be visible through the hole and illuminated by that exact point.
What we just invented is called Camera obscura, also known as a pinhole camera. You can take a shoebox, tape a piece of photographic film on one of the inner walls, punch a pinhole through the opposite wall, and have an extremely primitive but functional camera.
What's the point of expensive lenses, then? The primary issue is that only a tiny amount of light gets through that tiny pinprick. Thus, even on a sunny day and with a sensitive film, you would need very long exposures to get anything approaching a well-exposed image. If you enlarged the pinhole, more light would get through, but the picture would get blurrier. What lenses basically do is allowing a larger opening, with more light getting through, but still focusing the light from a single point on the subject to a single point on the film (or silver screen or sensor). They achieve this by clever application of the laws of optics (especially Snell's law) and geometry.
Another problem with very small apertures (as the hole letting light into a camera is called) is diffraction. Light waves traveling very close to a sharp edge get bent to some degree when they pass the edge. In photography, this results in a certain amount of blurring in the image. The larger the aperture, the smaller the percentage of light that is diffracted because most of the light doesn't pass very close to the edges of the aperture.
How does focusing relate to all this? Remember when I said that like a pinhole, lenses still project a point on the subject to a point in the resulting image? I wasn't entirely truthful. The thing is, with any realistic non-infinitesimal aperture, only light originating from a certain distance in the scene will have that point-to-point correspondence, with the images of points either closer to or farther away from the camera getting blurrier. By changing the distance between the lens and the film, you can change which part of the scene is projected sharply - that is, in focus. The larger the aperture, the shallower the part of the scene gets that can be said to be reasonably sharp.
For some very nice demonstrations of the above concepts, I recommend taking a look at the Flash applets provided as supplementary material of Stanford's CS178 digital photography course.