Explaining this to someone who has never been depressed is like explaining colors to a blind person. The experience is simply lacking to those blessed with good mental health. If the example of colors is too hackneyed, consider the difficulty of explaining the taste of a particular food to someone who has never tried it. There is a qualia to depression that cannot be communicated. Depression is not simply feeling really, really bad, although that is in many cases a prominent symptom. Nor is it merely feeling hopeless. Nor is depression any one thing. There are several symptoms that must be present in order for a case of "the blues" to merit a diagnosis of depression.
Psychiatrists use a list of symptoms, of which a certain number must be present for length of time. My own bias is to believe that no two instances of depression are ever quite the same. There are always differences in the specific symptoms as well as to their intensity, in addition each case's etiology is unique to thye sufferer.
That said, it is also true that cases of depression can be classified, categorized, and analyzed for their commonalities and differences. It is a dirty secret to psychiatry that the diagnosis and treatment of depression is an art and not a science. Part of the diagnostic procedure is questioning the patient about the presence, duration, and intensity of symptoms. Consequently, patience, insight and good listening skills are essential to being a good psychiatrist. These are all qualities in which some competency can be acquired, but more than a mere competency requires qualities of character. This means that there are personality types that cannot acquire more than the most basic rudiments of good psychiatry.
For all that, this doesn't mean that psychiatry is arbitrary in its diagnoses and categories. Psychiatry is properly speaking what psychiatrists do. The categories and criteria for diagnoses are the result of individuals with a certain type of training seeking to make sense of diverse but related phenomena. It is true, though, that a psychiatric diagnosis is because a psychiatrist says it is. The diagnosis, if it is a good diagnosis, will, when explained to other psychiatrists, appear reasonable and justified by the facts of a case. Facts here mean test results, observations, presentation of symptoms, etc.