The neurobiology of phobias is centered on the amygdala, a part of the brain which controls the fear circuits. So when you encounter a fearful or stressful situation or object, then your amygdala is activated and remembers the feared stimulus. Another part of the brain called the hippocampus also remembers the feared stimulus, and activates the fight or flight response via its direct connection to the amygdala, which starts the cascade of the stress response.
However, there is a last resort to stopping this activation of the fight or flight response...the prefrontal cortex can stop the activation of the amygdala. as it is directly connected to it. If the prefrontal cortex can't suppress the activation, then the amygdala activation continues with added activation from the hippocampus. Thus, fear conditioning proceeds, and ensures that the next time this feared stimulus is encountered, then it automatically activates the amygdala and the fight or flight response.
So the next time you encounter this same feared situation or object, then the hippocampus and amygdala remembers this stimulus and automatically activates the fight or flight response.