The idea is that depression could be a feedback loop in which negative life events cause the brain to become chronically flooded by stress hormones like cortisol and epinephrine.
These are pro-inflammatory factors whose chronic presence promote run-away inflammatory responses which kill glial cells, decrease neuroplasticity, retard neurogenesis, and also contribute to a whole constellation of other health problems like obesity, diabetes, and heart disease.
What closes the feedback loop is that this inflammation-mediated form of brain damage, particularly in the hippocampus and amygdala, directly compromise a person's cognitive ability to deal with life stressors constructively. The ability to process emotion, fear, and memory degrade.
Speaking a bit poetically, you could say that a severely depressed brain is one that has rewired itself to be a stress-processing circuit.
SSRIs no doubt work for some people, and the modern thinking is that they might be promoting neurogenesis through upregulating BDNF and other growth factors; there are multiple lines of evidence, one fun one is the fact that the maturation time of new neurons roughly matches the time it takes for SSRIs to start affecting depression (3-6 weeks).
Exercise also works, seemingly about as well as SSRIs for many people with moderate depression (Googling will provide examples of studies from the last few couple decades to that affect). I haven't read much about this but I would imagine that the metabolic and cellular stresses of a bout of heavy exercise (in which millions of cells die) promotes the production of growth factors all over the body, including in the brain.