RE-4: Dishonorable Discharge. We call it a Big Chicken Dinner (Bad Conduct Discharge).
When you separate from the military, you are issued a DD Form 214 that contains pertinent facts about your active duty military service, such as your awards, MOS, and discharge type. An RE-1 means that you completed your obligation as expected, called an Honorable Discharge.
Then there are "Other Than Honorable" Discharge types, and these have a letter code assigned to the RE code that tells background investigators exactly why you were discharged.
For instance, an other than honorable RE-2BLC discharge means that the military kicked you out for homosexuality. RE-2CBL indicates unsuitability for military service without a specified reason (usually lying to get in). The K's are usually drugs - the military tests you for drugs monthly. Even a puff of pot and you can face an OTH discharge.
The Big Chicken Dinner is reserved for the most egregious offenses of the Uniform Code of Military Justice (UCMJ), usually indicating criminal behavior: AWOL, drug abuse, stealing, acting in a manner that completely dishonors the military, and etc.
If you think of it in civilian terms, an OTH is typified by a misdemeanor, whereas a BCD is a felony (simple analogy).
Most employers will not touch you with an RE-4. It is MUCH worse than an Article 15 or 32. It means that the military criminally prosecuted you, found you guilty without doubt, and booted your butt out. You're irresponsible and embarrass the United States. You cannot be trusted.