Like a smartphone, a smart TV offers a number of "internet connected services" that normal televisions can't offer. It has the equivalent of a computer built into it, giving you a greater number of services. These televisions offer apps, media streaming, web browsing and games.
Smart TV is essentially the common name for a whole series of technologies. What you'll find in a smart TV are apps that give access to catch-up TV, such as iPlayer, All4, Demand5 along with film streaming including services, such as Netflix.
These days it's actually quite hard to find a TV that doesn't have some sort of media streaming functionality. TVs will often have an iPlayer app that will let you keep up with the BBC's TV and radio services via the Internet. But the reality is that smart TV can open up a whole new world of TV and entertainment that can reduce your reliance on broadcast schedules.