Varies with severity. Significance can vary with the extent of the collapse. If a large portion of the lung is collapsed then a patient will have difficulty breathing, which can be mild to severe, with respiratory failure and death as the extremes. Most often the collapse is limited and partial, often reversible with no intervention. Many things can cause collapse, so more information is needed from your doctor.
Potential danger. If the pneumothorax creates enough pressure, it can compress the right side of the heart. This decreases the blood return to the heart. Without adequate blood return, your heart does not have enough blood to pump out to your body. This can be rapidly fatal.