If all we do is talk, why shouldn't I just talk to my friends and family or go and punch a bag?

Doing all of these things can be reasonable and helpful ways of working on your issues. Sometimes though, without us realising, it's our continued involvement with the people around us that perpetuates our problems. Through their lives, people tend to find friends and situations that reinforce their own style of relating. Further, that style of relating is usually learned in the family (in other words, the continued presence of family and friends who reinforce your unconscious ways of relating keep on causing you trouble).

This means the people around you, with the best of intentions, have a vested interest in keeping you just the way you are even if that includes being unhappy. An example of this might be if you are the person in your family or group of friends who looks after everyone, always stays strong, always babysits, always does the odd jobs, always keeps the peace, never asks for anything in return or has any problems of your own. 
What group of people would want to give up such an asset?  If you never seemed to mind, why would anyone think you found it a strain?  If you often felt overwhelmed with everyone else's problems and wished for a change that someone would listen to you or do something for you, the people around you wouldn't be used to you ‘showing weakness’ by asking for help.  It wouldn't seem like the same person they knew and could always depend on and it may also make them worry that they're losing you in some way (not necessarily that you're going away but maybe that you won't be as willing to do favours).

In these situations, people around you often find the change in you difficult and resist it, even if in the kindest possible way. If you complained to them, for example, about everyone always asking to be go-between or getting you to do favours and never caring about how you are, whether you're tired or ill or upset, their response may well be along the lines of, 'but you're always so strong' or 'don't worry, you'll be fine'.  They don't mean to but in a way, they are refusing to acknowledge your personal needs which sometimes you really need them to see.

The key thing to understand about these kinds of scenarios (and one of the hardest to grasp) is that you YOURSELF often don't even know you're doing it.  You become who you are 'today' through the gradual build-up of millions of influences over years.  Just like walking or driving, the ways you perceive other people (what you believe they think of you, what you believe they think of themselves, what you believe they expect of you and what you expect of them) are consciously learned (often while you're very young) and then they become unconscious; you just do them without thinking or even realising. 

The reason this is hard for people to grasp is because it's not tangible.  I find it best to think about it like learning to walk, drive or play an instrument.  At first you painstakingly learn every movement and all the coordination but after a while, it's automatic.  It's the same with learning to be with people (in all the ways that we interact, at work, at home, socially and intimately).  It might seem looking at statistics and the way communities generally work that everyone does it the same way but when you look more closely at individuals, there is massive variation and it's in this variation of the finer details where psychotherapy works.

Psychotherapy is another type of relationship.  Think about it like this, if these are types of relationship: 'friend', 'partner', 'immediate family', 'extended family', 'colleague' then 'therapist / client' (or ‘psychotherapy’) is just another type.  The purpose of the psychotherapy relationship is to learn about your  unconscious ways of relating and general 'world view'.  This knowledge is then used to understand how these learned ways of relating cause problems for you when relating to others and finally as you come to understand yourself more, you can begin to see what part you play in relationships with others and so how you might change to get more of what you need in those relationships.  

The psychotherapy relationship promotes this kind of exploration and change because it is private and confidential and your therapist is ethically bound to avoid conflicts of interest (for example, having their family members, friends or colleagues as clients or seeing two partners for separate individual therapy - notwithstanding couples therapy).

One reason for this is to allow your therapist, as much as possible, to be there for the you without prejudice, that is, without a vested interest in your situation outside therapy.  An example of your therapist having an inappropriate vested interest might be if you and your therapist had common friends and you mentioned issues involving your friends in the sessions.  In this case, it would be very hard for your therapist not to judge you (put you 'in the right' or 'in the wrong' or decide you 'hadn't done enough') and further, it might even be tempting for both of you to just use the session as a time to gossip about common friends or family.

The idea of conflicts of interest does not belong solely to the psychotherapy profession. Another example would be in law where before a firm or individual solicitor takes on a new client in certain cases (such as a divorce), they will not represent both parties and may also check whether they have previously represented the other party.  In psychotherapy, the checks are less stringent but the idea is similar.