The Measurement Scale property controls how measurement values of dimension labels are scaled to their actual length. It also affects how typing in lengths or coordinates is interpreted, but only if Use Measurement Scale is enabled.
You can think of a Blockpad drawing canvas as a physical piece of paper, with the dimensions specified by the Canvas Size property. Thinking of a normal 8.5 in x 11 in paper, if you print out a canvas of that size, you can measure the lines on it, and that is the actual geometry size in Blockpad (if the canvas scale is set to 1).
If you think of the canvas as a piece of physical paper with the size specified by canvas size, then the Measurement Scale is like the dimension labels are using a scale ruler instead of a normal ruler.
If the measurement scale is 1, then the dimension labels in a Blockpad drawing will show the actual geometry length (unless their text was modified). If you have a canvas size of 8.5 in x 11 in, and a 2 in line on it with dimension labels, the label will show 2 inches and you will measure 2 inches when you print the page.
If the measurement scale is not 1, the actual geometry will not change, but the value displayed by dimension labels will be multiplied by the measurement scale. In our 2 inch line example, if we set the measurement scale to 5, the line will still measure 2 inches on the physical paper, but the dimension label will show 10 inches.
All of this applies only if the Canvas Scale is set to 1. The canvas scale changes the size of the actual geometry relative to the canvas size (the piece of paper), so it can confuse the relationship between the measurement scale and the "piece of paper". It's suggested to keep the canvas scale set to 1 for any drawings where printed scale is important. The canvas scale is useful for resizing drawings where printed line measurements are not important.