A military discharge is given when a member of the armed forces is released from their obligation to serve.
Discharge or separation should not be confused with retirement

Retirement

Retirement is the point where a person stops employment completely. A person may also semi-retire by reducing work hours.Many people choose to retire when they are eligible for private or public pension benefits, although some are forced to retire when physical conditions don't allow the person to...

; career U.S. military members who retire are not separated or discharged; rather, they enter the retired reserve and may be subject to recall to active duty.

A discharge completely alleviates the veteran

Veteran

A veteran is a person who has had long service or experience in a particular occupation or field; " A veteran of ..."...

 of any unfulfilled military service obligation, whereas a separation (which may be voluntary or involuntary) may leave an additional unfulfilled military service obligation (MSO) to be carried out in the Individual Ready Reserve

Individual Ready Reserve

The Individual Ready Reserve is a category of the Ready Reserve of the Reserve Component of the Armed Forces of the United States composed of former active duty or reserve military personnel, and is authorized under...

 (IRR).

Below are some of the most common reasons for discharge:

• Expiration of Term of Service (ETS)
• Reaching the maximum age limit
• High Year Tenure (reaching the maximum allowable time-in-grade, and not selected for promotion)
• Disability, Dependency, or Hardship
• Pregnancy/Parenthood
• Personality Disorder
• Condition not a disability
• Physical or Mental Conditions that interfere with military service resulting in being placed on the Temporary or Permanent Disability Retirement Lists
• Convenience of The Government/Secretarial Authority (voluntary redundancy
  Voluntary redundancy
  Voluntary redundancy is a financial incentive offered by an organisation to its employees with the purpose of attracting volunteers to leave the organisation, due to downsizing or restructuring situations. The purpose is to circumvent union employee regulation laws.-Reasons:A Voluntary Redundancy...
  
   due to funding cutbacks, for example)
• Unsuitability
• Misconduct - Minor Disciplinary Infractions
• Misconduct - Drug Abuse with and without administrative review board
• Misconduct - Commission of a serious offense
• Entry-Level Performance and Conduct
• Resignation (available to officers only)
• Reduction in Force (RIF)
• UnCharacterized if discharged within the first 180 days of service and no misconduct found in service members record
• Punitive Discharges - Bad Conduct Discharge issued by either Special Court Martial or General Court Martial only.