The school that I want to attend wants me to write a letter explaining why I am interested in the program?

When you are involved in an application process and you run into a requirement like this one, its purpose is to find out about your writing skills. The school already knows why you want to attend there. They're already aware of your desire to "further your education." They're looking for two things. The first is whether you can organize a piece of writing properly. They want to know if you will have an introduction, body paragraphs, and a conclusion. The concept of "passion," which others have suggested, is fine, but the point is to translate that passion into an organized, logical piece of writing. My recommendation would be to think of three reasons why you developed a "passion" for the health care field, make each one the focus of one of your body paragraphs, and develop your essay that way. For example, the first body paragraph might be historical. "I started dreaming about helping others from the time I was in grade school." Then you tell about it. Your second paragraph might be something like, "Making a contribution to society is an important part of my life," then you explain it. See the idea? The second thing which the school is going to consider will be the grammar and mechanics of your essay. If you are not really, truly confident about how you express yourself, then have an expert look over the letter before you send it. Don't rely on computer spell checkers or grammar checkers. They're not reliable. If you do not personally know the answer, have your work proofread by a teacher or trusted friend. Taking the steps I have recommended should get you good results.

Do you have a passion for the field? Why? Describe it. What reasons did you get into/stay in the field? Don't say you're applying just because it makes sense and is the next logical move. They want someone who is driven by something more than just obligation.

I agree with Nick