To "discharge" someone is to release them from something. As Jimmy said above, this can include being released from military service.
It can also be used in the context of releasing a patient from the hospital. In that case, the discharge orders might include items such as why the patient was in the hospital, what medications they received while there, what continuing treatment (if any) has been recommended, etc.
The related term "order of discharge" is used in a legal context in finance law to release a person from their financial obligations.
I hope that helps!