First, check the metadata associated with the raster data for obtaining cell size and other related information. However if there is no metadata (not a good practice) then you can check the cell size in the data source tab (under properties).

I fully agree with Mr. Sivanpillai and could not answer better your question. So, check the metadata, if there is no metadata, use the information of the cell size in the data source tab.

here is the answer

How do I determine the units of those dimensions? Is it always in meters?

Not necessarily. Scroll down a little further in Properties > Source, until you see 'Spatial Reference'. There you will see the unit for the data layer. Good luck.

Ramesh Sivanpillai what's the usual pixel size unit in ArcGIS Pro?