What is, formally speaking, major depressive disorder? DSM and ICD define a mental disorder called major depressive disorder (MDD), and I suppose the notion of MDD defines quite rigorous criteria and methods to diagnose it in people. I don't know, how MDD is defined, what is its criteria, what are its diagnostic methods. On the other hand, cognitive behavioral therapy practitioners, such as David Burns, define depression through the use of rating scales.

For example, David Burns has a questionnaire, called Burns Depression Checklist (BDC). It asks you 25 questions about various thoughts and moods you experienced at least once during the week. Then it asks you to assign a number from 0 to 4 to each of them, meaning how strongly you experienced it, 0 meaning “not at all”, 4 meaning “a lot”. Then you add the numbers up, and if you get more than 10, you have a depression: mild depression (11-25), moderate depression (26-50), severe depression (51-75), extreme depression (76-100). The questions are very different, they ask if you feel sad, or discouraged, or worthless, or guilty, or lonely, or demotivated, or sleep to much, and so on. Therefore you can have different combinations of physical and emotional symptoms, and still have depression according to BDC. For example, i could put number 4 to questions about guilt, hopelessness, and self-esteem, yet put number 0 to questions about motivation, interest in work, and feeling tired; or I could do the other way around, and it would still mean i have a mild depression.

According to the study called The Epidemiology of Major Depressive Disorder, 16.2% of US citizens experienced MDD in their lifetimes. If we assume Burns's definition of depression through result of BDC scale, then this study's data contradicts common sense and my anecdotal evidence. I gave BDC to various friends of mine, and all of them showed at least mild depression. From behavior and self-accounts of many people I meet every day I can safely assume that mild and moderate depression (in Burns's definition) are the statistical norm; the depressed people are the majority of population. I understand that anecdotal evidence means nothing.

My question is as follows. What exactly is major depressive disorder? How it is defined in a formal way? What are the criteria, which a person should met, to be diagnosed with MDD? What are the methods to diagnose it (for example, do psychiatrists use rating scales like BDC)? Finally, how MDD is different from the many alternative definitions of “depression”, including the colloquial ones?

I ask this because I can't reconcile my intuitive hunch that most people around me are depressed, some of them heavily, yet studies show that depression, while serious, isn't that widespread. If MDD is defined in a very different way, than Burns's depression, then it would mean that only a minority experiences MDD, so there's no contradiction.
The ICD and DSM definitions can be a bit opaque, but there are several criteria that are usually considered necessary for diagnosis. Different practitioners may diagnose more conservatively or more pervasively, but those differences are based on their professional experience, and they are all meant to interpret from similar guidelines. Because there are different severities of depression, as with any illness, diagnosis relies also on the subjective judgement of a doctor or other mental health practitioner. 

Generally, if one experiences a persistently low mood and low energy for a period of longer than two weeks, they may be diagnosed with so-called "clinical" depression. Usually this entails disruption to one or more aspects of daily living, e.g. food, sleep, interpersonal relationships, work or hobbies. This type of disruption is sometimes termed "clinically significant distress", a fairly common criterion for mental illness. 

Prevalence is difficult to accurately assess. The NIMH reports 6.7% 12-month prevalence in the US. The CDC has a map of US states showing statistics for current depression, ranging from under 5% to as high as 15%. Other statistics exist in other countries. These data may reflect the best methodology available, but they are still fallible. Epidemiology of mental illness is a difficult field of study. 

The inventory you cite is one of several commonly used ones. It's also important to remember that a psychiatrist will not rely on self-report questionnaires for diagnosis. A doctor would conduct a thorough intake interview which takes into account many other factors. A fifteen or twenty question survey is not sufficient to definitively diagnose anyone.