What does a mm of rain mean? Lots of people have explained it over many sites but I still can not confidently say that I know what it means when they say Hong Kong experienced 3mm of rainfall last Friday.

Does it mean that 3mm per square meter was experienced in a specific area, or does it mean that the total amount of rain had a volume such that if it was spread over all of Hong Kong the height would be 3mm. Or is it referred to in terms of per square meter?

What is the time period? Is it measured per day, per hour, per minute?

EDIT: The question marked as a duplicate may refer to some aspects of the question but does not effectively ask them. The title of the question refers to something different and the only answer to that question is what I am asking an explanation of.
It's confusing to measure liquid in units of length instead of volume, isn't it? Here's how it works.

"One millimeter of rain" is actually one cubic millimeter per square millimeter. On average, over the area you're talking about, each square millimeter has received one cubic millimeter of rain. If you divide n mm3 by 1 mm2, you get -- n mm!

The field of Dimensional Analysis deals with questions like this.

If there was "1 mm of rain", how much rain did a square meter receive? 1000 mm * 1000 mm * 1 mm = 1 000 000 mm3 = 1 liter. Pour one liter of water into a square container one meter on a side, and it forms a layer one millimeter deep.

To calculate "how much rain fell on Hong Kong" (expressed as total volume), you'd take the area of Hong Kong, and multiply it by 1 mm. That's usually not what people want to know, though -- they want to know how wet things got, and the volume-per-area number is most convenient for that.