Sum Insured (SI) is the maximum amount that is provided to you (the insured) in case you make a claim due to a medical emergency, treatment for illness, etc. It is directly based on the concept of indemnity.
So, when you make a claim, you will get a reimbursement for the costs spent on the medical treatment. If the cost of the treatment is less than or equal to the sum insured, the insurance company will cover the entire bill amount. However, if the costs of treatment or hospitalization exceed the sum insured, you will have to bear the extra cost beyond the SI yourself.
In short, the sum insured is an indemnity-based reimbursement you can get in case you make a claim with your health insurer.
All non-life insurance, like health insurance, home insurance, motor insurance, etc. offers this sum insured.