Finally, something on PPOT that I know a little bit about
Simplifying things a bit, an MRI system has two magnets.
The big one: which causes the water molecules in your body to resonate. This is called the main magnetic field and is (very) uniform and constant.
And a smaller one which allows some regions to resonate and not others. This is called the gradient magnetic field and is switched on and off rapidly.
If the system only had a main field, all regions of your body would generate data at the same time. For an analogy think about walking into a stadium and asking, "what is your name?" and 80,000 people answered at once.
With the addition of a gradient field, most of your body is detuned and only a small volume is allowed to resonate. To extend the stadium analogy, lets say you asked "section 3, row g, seat 22 - what is your name?" and one person answered.
The noise results from these two fields interacting with each other. Generally speaking, as MRI systems become more sophisticated, they make more noise and at a higher frequency.
As an aside, the signal emitted from your body is tiny, much like one voice in an 80,000 seat stadium