The more technical name for the piano and guitar finals is "piano jury" and "guitar proficiency". The piano jury is basically to prove I've actually learned something this semester, so I have to go before a panel of my professors, play through a couple of the pieces I've learned this semester, and answer some questions on them. The guitar proficiency is similarly to prove that I've learned the necessary skills (song memorization, ability to play in a variety of styles, ability to change how I'm playing at a moment's notice) on guitar.
I'm not going to be a music therapy student starting in the spring semester, but basically - music therapy is the use of music and music-based interventions to elicit change in a person or a group. (I have to define music therapy on my final exam for Music in Therapy so this is a good practice! :p) But more specifically, music therapists work in all sorts of settings - at schools, in special education, in psychiatric settings, in nursing homes or group homes, in hospitals. In all cases, the goal is to use music to help people in some way. This goes beyond just walking into like a hospital room and playing the patient's favorite song (we call that "music entertainment") - we have specific goals for the clients we see. Like, if someone were in a hospital bed and were being unwilling to move their hands, we might use our guitar or percussion instruments and be like, "Hey, reach out and play this!" - our goal, then, is "increase physical movement".
My example I like to use when explaining it is with my client last spring. At my school, we see actual, paying music therapy clients at a private practice clinic, and every student is assigned a client to work with (with a certified music therapist supervisor's help, of course!). Most of the time, these clients are children, teenagers, or young adults with physical or developmental ailments - Down syndrome, autism, etc. My client last year had apraxia, which means he had a lot of trouble coordinating his muscle movements, resulting in difficulties with fine motor skills and somewhat garbled speech. He had a tendency to move his pinky and ring fingers as one unit, and I was trying to discourage this by having him play the piano, and telling him to use certain fingers for each note. By the end of the semester, he was able to move his fingers independently and very quickly, to the point that my supervisor was absent one week and when she returned she was astonished at how quickly he had improved since she had last been there!
It's a really great practice. I'm just leaving because my heart isn't in it as much as I would like.