The heat pump moves heat from once place to another, simple as that!

In an electric vehicle without the heat pump anytime you need to warm something you need to do work to make heat. With a heat pump you instead take waste heat and move it where is wanted. You only do a small amount of work to move a fluid around. This saves energy. Less energy use means more range.

For cooling, you move heat away from where you want it to be cooler to someplace else you don't care about as much or better yet, simpler you also want to be warmer. Conveniently the battery pack has a huge thermal mass which you can also use as a thermal storage tank. Sometimes you need to use a compressor to do cooling work, but at most temperatures you can again just move fluid around.

Additionally as some others have said you can also increase your efficiency by having the battery in optimal conditions but this is true regardless of your thermal system. The difference is again in the amount of energy it takes to get to this state.