In people with anxiety disorders, the brain circuitry that controls the threat response goes awry. At the heart of the circuit is the amygdala, a structure that flags incoming signals as worrisome and communicates with other parts of the brain to put the body on alert.
Early life events, especially traumatic ones, can impact the circuitry so that it is oversensitive and sends out alarms too frequently. We have to perceive threats in order to survive, but those with anxiety see threats where there aren't any, perhaps because emotional memories color their perceptions.