It's often used to indicate an elevated or abnormally high level of something. For example:
* Hypertension: High blood pressure
* Hyperglycemia: High blood sugar levels
* Hyperthyroidism: Overactive thyroid gland
* Hyperplasia: Increased cell growth and division
* Hypertrophy: Increased size of an organ or tissue
Essentially, hyper- signifies a condition where something is exceeding its normal range or limit.