When I was taking graduate-level mathematics courses, my professor told me that abstract concepts become much easier to wrestle with if we make them real through focused realization and imagination. This has served me well.
We understand the world through our senses and our body. The best way to understand an abstract concept is to turn it into something that we can visualize or somehow "feel" in a tactile way.
For example, sometimes functions feel like a dance to me. The movement of the dance represents the transformation of the domain to the image of the function.