In 1984, the telescreen is a tool used by the Party to detect instances of rebellion. You will notice in Part One, Chapter One, for instance, how Winston keeps his back to the telescreen when writing in his diary. This is to prevent the Party from seeing his diary because he knows that if they found it, he would face some harsh and violent punishment, like a forced labour camp.
That the telescreen cannot be turned off (except by Inner Party members) gives us another glimpse into its purpose. The telescreen is designed to monitor every movement and capture every conversation between Party members, whether they are at home, at work or in some other public place. As such, the telescreen also functions as a deterrent against breaking the rules. People are far less likely to commit a crime, for instance, if they know that Big Brother is indeed watching them and that they have little chance of getting away with it.