It's not friendship. There are friendship qualities like communication, mutual respect, support and the sharing of feelings involved, but that's about it. You won't be having your therapist over for a barbecue, or calling her on the phone to chat while you wait in line at the DMV, or sending him funny e-cards.
It's not a priest/pastor/rabbi/shaman relationship. You may choose to discuss spiritual issues, experience epiphanies, or confess transgressions, sure. But therapists don't absolve sin and don't typically act as God's mouthpiece.
It's not a medical relationship. The two of you are meeting to try to resolve a problem that causes distress, thereby relieving pain, but the interaction is different from the medical model. While it might be appealing for us to go under anesthesia and wake up to find our depression floating in a jar of formaldehyde next to us, therapy requires a more action from the client.
It's not a pep talk. Some folks evaluate the effectiveness of their therapy by asking "do I feel better after the session?" Often, the answer is no. For starters, things often get worse before they get better in therapy - you may enter with a problem and then realize after a few weeks that the problem is deeper and more serious than you thought. This doesn't always feel good. But with patience and effective treatment, you'll start to feel more clarity about the issue, and therefore more control over it. A perpetual state of happiness is not the desired outcome from therapy - that would be an impossible goal. Greater awareness of yourself, access to your thoughts and feelings, and control of your behavior is a more realistic outcome.
So that gives us a glimpse of what it's not, let's look at a few ideas about what it is.
It's like a personal trainer relationship. People go to personal trainers with a goal - lose weight, get toned, drop a dress size, whatever. The trainers work with you to develop a plan of action, stand next to you as you do the work, give encouragement, and revise the plan if obstacles arise. It's collaborative, but notice the different roles: trainers use their knowledge and experience to guide the process, but you do the physical work and reap the benefits.
It's like a mirror. We often have a hard time seeing ourselves accurately, and sometimes our friends' and family's feedback is more about their issues than ours. Therapists are trained to see a person as objectively as possible. They may see things in your thoughts or behaviors that other people don't or are unwilling to tell you. It's not uncommon to hear a client say "I had no idea I did that - no one ever told me."
It's like re-parenting. I'd better tread lightly here. I'm not saying that therapy replaces parents, or that parents are bad at their job - "blame the parents!" is a tired old battle cry in psychology. What I am saying is that sometimes therapy helps fill some gaps or re-tool some messages we heard in childhood. A man may have had a great relationship with his parents, but their difficult divorce left him unclear about how healthy relationships work. A woman may have grown up in a family where expressing emotion was taboo, an old rule that causes problems in her adulthood. The therapist can represent a different voice for the client, one that guides them toward healthy relationships and behaviors.
More than any of the above descriptions, however, every therapy relationship is unique. I've met with hundreds of clients in therapy, and no two relationships are exactly alike. Talk about what you want it to be, then make it so. It might be one of the most important relationships you'll ever have.