Amélie's television delivers a variety of news to her, sometimes real, sometimes all in her head.
Princess Diana's televised funeral kicks off Amélie's journey. In shock at the news, Amélie drops her perfume bottle lid, which cracks the tile, which reveals the tin, which swallowed the spider, which swallowed the fly, etc., etc. Although Amélie does get out to see the world, she also keeps herself pretty separate from it, so it's no surprise that she gets one of her greatest shocks not from something in her own life but from something she sees on TV.
Amélie also often records things she sees on TV to deliver to Dufayel, who can't leave his apartment and doesn't ever watch TV, either. (So he's one step even further removed from the world than she is.) It's a way of giving him a glimpse into reality.
Sometimes the TV gives us a glimpse into the reality inside Amélie's head, which doesn't quite match what's going on in the real world. For example, she imagines she collapses from exhaustion from doing good deeds and then envisions a massive TV funeral, but even though we see it with her, it's all a fantasy.
However, it's back to reality in the end, when for once it's Dufayel who sends a tape to Amélie, rather than the other way around. Dufayel's tape encourages Amélie to do what he can't—to get outside the apartment, and outside her head, and live a life in the real world. And she does.