Your question hits one of the main purposes of terrorism. The psychological effects of terrorism are powerful.
When terrorists strike, they obviously want to cause destruction and take life, but they also want to strike fear into a society. This can cripple a country's economy. Yesterday there was a terrorist attack in Thailand and one of the aims of the terrorists was to cripple its tourism economy, one of the bright spots in the region. If the terrorists succeed, it will hurt many people. This is partially what the terrorists wanted to do when they struck New York on 9/11. Unfortunately, at times terrorists succeed and people are gripped with fear.
There are also unintended psychological effects of terrorism. To use 9/11, as an example, Americans became closer as a result of the attacks. People from around the country travelled to New York to help, and many New Yorkers got back to work the next day, as a message to the terrorists. American became closer.
The psychological effects of terrorism is to strike fear into the heart of those being terrorized. The terrorist are wanting to defeat those they are terrorizing and by putting fear in them so they can control them. The psychological effects on the one being terrorized is fear. They live in a constant fear of danger as well as feeling they have no real control over their lives. The one that has been terrorized is constantly look over their shoulder as they do not feel safe and their brain is in a high stress response anticipating something "bad" to happen. The fear that has been invoked does not leave even after they are no longer in a terrorist situation. They suffer from all the symptoms of post traumatic stress and can be jumpy or react without warning in certain situations. They will have feelings of anxiety, fear, sadness, and more. The effects of terrorism is horrendous and depending on the level of terrorism felt will take months to years for recovery to happen if ever.