Good question. I am assuming that you have a JAG Defense Counsel at the Area Defense Counsel's office. I am also assuming that your commander decided to discharge you - and there can be multiple reasons for that, and it should be on your "Notification" paperwork informing you why he or she is recommending you for discharge.
Remember that you are being discharged with a General Discharge (under honorable conditions). Depending on how long you have been on active duty, it MAY affect some of your Veteran's Benefits - you will have to check with the VA for your specific eligibility.
The biggest impediment job wise that you will face is that you will be ineligible for most government - federal, state and local - jobs, although again, you may seek a "waiver" based upon your specific circumstances.
A background check generally will not show your military experience UNLESS you were charged and convicted in a court-martial. Administrative discharges are not generally entered into the "system." But, most employers ask: "Have you ever served in the Military? If so, what type of discharge did you receive?"
Note, that lying about this is in most states, grounds for automatic termination.
If you have any more specific questions, talk with your ADC.