Intuitive explanation of precipitation amount
It literally means that the water depth will be 0.5mm. For example, if you place a container under the rain and it fills up to 0.5mm, then the precipitation is 0.5mm.

Despite the fact that a wide container requires more rain to fill up than a narrow container, the larger surface area allows it to collect the right amount of rain water to fill up to the same amount as the narrow container in the same amount of time (as long as the walls are vertical). Therefore, if the rainfall is 1 mm, every square meter receives 1 liter of rain water.

Addendum:

By the way, tuna cans can be distributed along your lawn to serve as a very primitive, but very cheap measurement tool that you can use to create a spatial map of what your irrigation system is doing. You can use that for troubleshooting your efficiency, 1 full can is 1 inch irrigation/rainfall.