It is a wide topic, but one of importance. The idea of existential angst is central. I have read Kierkegaard's 'Fear and Trembling', and found it worth reading, but it is probably rather obscure for most present day experiences. In thinking about depression, they frequently involve feeling 'bad' and 'sad', but have become medicalised, so it is worth thinking of the medical model of depression.
There is definitely a physiological aspect to it, especially in relation to neurotransmitters, which is why antidepressant drugs are given. However, a biopsychosocial is useful in considering the way in which experiences in life and social circumstances affect mood.
The understanding of depression also occurred in the context of psychiatry and the development of psychology. Many view psychological therapy as being important, often in conjunction with antidepressants.
Psychoanalytic theory has been important in thinking of depression. This is a vast subject area and one aspect of which Freud may have made a significant contribution is in the inability to moarn. This would include deaths of others, but also, the traumas and 'deaths' of painful experiences. One other area which it may be worth you reading about is Melanie Klein's idea of the depressive position, which involves a sense of guilt. This occurs in the early life experience of perceiving the mother and oneself, but is relevant for all life experiences. The topic of psychoanalytic theory, and its criticism, is so vast.
There is also the cognitive behaviourist approach, which emphasises that it is not experiences in themselves which lead to depression. It is our beliefs about experience which trigger feelings. So, cognitive behaviour therapy involves looking at and questioning beliefs about experiences. In some ways, CBT is a philosophy approach to understanding experience and it has parallels with Stoic philosophy.
The whole philosophy of emotions is also relevant. Also, the philosophy of mental states and moods may draw upon multidisciplinary thinking, including both the sciences and the arts. Some critics of the medical model see it as being a limited view to simply prescribe medication to lift one's mood. However, this is also open to criticism as in 'clinical depression' the severity can result in an inability to function, to eat, wash and the presence of suicidal thoughts.
There is a whole spectrum of experience in thinking about what is depression? The word may be used by individuals to describe varying experiences, including the presence of a 'blue' or 'black' mood. It includes unique experiences although it involves a universal sense of misery and potential for a state of despair. There is also the question of what makes life worth living and what is happiness?