The "mechanism of change" is an industry term for what makes change occur. Of course, each theory has a different opinion.
What your therapist believes is the mechanism of change should be included in the informed consent, either on a written document or during the first conversation. Although therapists will often refrain from answering certain questions, preferring to have the client answer instead, this piece of information should be readily supplied. Therapy is difficult enough without having to guess how your therapist thinks change will occur.
My own mechanism of change aims at the deepest parts of personality that are still amenable to change. Some theories (like cognitive-behavioral therapy) want to change how you think about your situation; a change in thinking will promote a change in action and hopefully a change in feeling. Other theories try to change the environment. Family therapists and social workers are two groups of people who take an active interest in changing the environment around their clients, whether the family or society.
My approach is a bit different. I believe progress comes from two sources: the therapeutic relationship and the event of therapy. In the relationship, the client is ideally given the sense of being understood. This is the easiest state of mind from which to begin thinking differently about one's life. The event, on the other hand, is a promise: it will be there the same time every week, for the same duration, and with the same purpose. With this support in place, people are more likely to risk change. If something doesn't work out, we can always talk about it next session.