Why do partial braces have or need the rubber bands?

Makes it work better: Rubber bands are used to help teeth move in the desired direction. These allow the teeth to move with more control.

Rubber bands: Malocclusions are like snowflakes, no two are exactly alike. Orthodontic specialists have training and experience that allow them to choose from a plethora of treatment modalities. Elastics are often used to facilitate reciprocal movement. As to your particular circumstance, ask your specialist Orthodontist what he/she is trying to accomplish.