I've been diagnosed with recurring depression and there is quite a lot of that in my family line (father is currently medicated after years long serious depression, etc.). There have been times I've been depressed and not went for treatment and there have been times I've went to a therapist... and there is a world of difference. Of course, depression affects individuals in different ways so everything I say might not apply to everyone but I'll try to speak on a relatively general level.
First of all... "Time, improving life circumstances, and new friends are what end depression"... Those aren't the kind of things that happen during a depression! When you can't force yourself to get into the job (a job you normally love, really want to keep, etc.) in time (or at all) for months and even if you get in, you can't concentrate enough to do anything complex (e.g., coding) efficiently... When you don't feel any interest to meet friends, girlfriend, etc... there's pretty high chance of getting fired, failing your classes, destroying your relationships, etc. which will make the depression deeper. Time might take care of it but if you allow that situation to go on for months first (untreated, my depression usually lasts about 4-5 months), you've probably nearly ruined your life first (been there, done that).
So, if you're depressed, not getting treatment is usually stupid. There are always medications but studies have shown that if you treat your depression with drugs, you're likely to get depressed again sooner and the next depression is likely to be deeper... until the medicines don't have enough effect anymore.
As for what happens in therapy... I've been to quite a few sessions and I've never had to talk about my childhood and whatnot. There are quite a few schools of therapy but Freudian, Jungian, etc. exist only in movies and as fashionable things to try out for the rich people. The therapist I usually go to helps me do damage control: Helps me take the steps that prevent me from ruining my life (Talk with my boss about my need to work at a reduced capacity for a while instead of me just not showing up for work half the time, etc.) at first and then helps me claw my way out of the pit (prioritize the massive bulk of tasks that seem impossible to handle, get small successes on which to build, etc.), helps me find the things that deepen my depression and find ways to solve them (Your home is filthy? You don't think you're going to lose your job immediately? Well, get a cleaner to visit it once a week until you're up and going again!... type of practical solutions)... Nothing magic but just things that you can't get done without help if you're depressed.