An emotional barrier was a negative feeling or belief that made it difficult to communicate clearly and effectively.
In 2368, Jean-Luc Picard said to Data, "Father and son. Both proud, both stubborn, more alike than either of them were prepared to admit. A lifetime spent building emotional barriers. They're very difficult to break down. And now the time has come, it's too late. It's a difficult moment. It's a lonely one. It's a moment Spock is about to face." (TNG: "Unification I")