In 1984, who are the Thought Police and what is Thoughtcrime?
In 1984, the government, or the Party, is a very controlling force in the lives of the citizens. It puts up cameras everywhere to watch the people, and to enforce good, patriotic behavior. So, no matter where you go, you are always being watched. That way, if you say something negative against the Party, it is recorded, and the government comes after you. It is wrong to say anything against the Party, to rebel, or even to not be super-enthusiastic about the Party in any way. And, it isn't only actions and words that are punished; they attempt to punish even your rebellious thoughts.
So, the Thought Police are the people hired by the government to monitor all of the screens, and to hunt down and find anyone who has committed crimes against the party. Those crimes are speaking out, not participating in activities, appearing to not enjoy Party activities, and even thinking badly about activities. How do they monitor thoughts? Well, sometimes when you are sleeping, you talk in your sleep, and those words reflect your inner thoughts. Sometimes, you might hesitate before chanting a Party ritual. Sometimes, you might not be yelling out hatred during the set-aside Hate times during the day. Any hesitation, any apparent lack of enthusiasm or patriotism, is considered Thoughtcrime, becuase it indicates that your thoughts are rebellious, that in your head and heart you aren't loyal to the Party. So, the Thought Police punish you not only for blatant crimes, but subtle things too, labeled as Thoughtcrimes. It's a pretty scary situation, and one that stresses Winston out. He is always worried that the Thought Police are going to know that he hates the party, and come after him. I hope that those thoughts helped; good luck!
In this book, Thoughtcrime is just what it sounds like. It is the crime of having incorrect thoughts. In the case of this society, it means having basically any thoughts that are not approved. So Winston is committing Thoughtcrime when he writes "Down With Big Brother" because that is not a thought that is permitted. But it doesn't even take anything that overt -- you can be guilty of thoughtcrime just by talking in your sleep (if you say the wrong thing). You can even be guilty of Thoughtcrime if you feel sexual desire.
The Thoughtpolice are the people who enforce the laws against Thoughtcrime. They listen to people's phone calls, watch them on the screens, etc.