When a painter (picture, not house) sticks her thumb up and squints over it at whatever she’s painting, what exactly is the purpose of the thumb?
measuring distant items. The thumb is always held at arm’s length to keep it consistent, of course.
To add some detail to Sapo’s answer, I’m an artist and when I do that, I’m not really looking at my thumb, I’m holding a brush or pencil and using the distance from end of my thumb to the end of the brush to measure the height or width of an object in the distance relative to the height of something else. As in, “The barn is twice as wide as it is tall”.
So it looks like you’re comparing things rather than measuring, am I right? LIke - “yon barn appears to be two-thirds the size of my thumb nail”. But how does knowing that help you get it right on the canvas?
I was wondering how a thumb could be used to measure anything to any degree of usefullness. Otherwise why not just hold up a ruler, or why not etch lines or rings into the brush end of the paint brush.
<runs off to patent office>
Yeah, you’re not really looking at your thumb at all, you’re just using it to indicate a spot on the brush handle, as in, “The barn is from here to the end of the handle tall.” You could use a ruler or your handy dandy patented Brush With Lines Drawn On The Handle (my, you’re quick!) to do that, but I’m still going to indicate which line is the right one by holding it with my thumb.
The way it helps with the actual canvas is this. Say I want the barn in my painting to be this tall. How wide will it need to be to be in proportion to the real barn, then? I measure the height of the real barn at arms distance on the brush it ( cuz I have a brush in my hand already), then I turn the brush sideways and see that the barn is three times the height wide. So I need to make my painting of the barn three times wider than it is tall. I don’t want to use a ruler and make precise measurements and calculate the ratios of a bunch of fractions, because I’m an artist, thank you, I don’t do math if I can help it. 
I mark a new distance on the brush to match what I want the barn’s height on the canvas to be and mark off three of that distance wide on the canvas to show how wide to paint it. I’m going to do the same thing with trees and fences and cows and whatever else I want to put into the painting.
It’s the ratios that you’re figuring out. So basically, IMO when artists are shown in movies or cartoons looking at their thumbs, it’s either a joke or a mistake.