The phrase "to polish up" means to improve or perfect something by making small adjustments, refining it until it is in its best condition. It can refer to cleaning and shining an object, such as a piece of jewelry or furniture, using a polishing cloth or compound. However, the phrase is also used figuratively to mean enhancing one's skills, knowledge, or appearance by studying, practicing, or taking care in presentation. For example, someone might say they are "polishing up" their public speaking abilities by attending workshops and practicing regularly.