Literal Translation
To eat on the thumb
Actual Meaning
To eat on the go, really fast
Etymology
This expression has been in use since the early 19th century.
First, think of the workers of yesteryear who, having brought their meals in their lunchboxes, had very little time to eat, or of soldiers at war who, while on the move or waiting to be bombarded or attacked, had to quickly swallow their meals.
Now imagine one hand holding a piece of bread (or something else edible) and the other holding a knife with which the eater cut a piece of food, pushed it onto their thumb and held it there while bringing it to their mouth.
That’s about it, if you can picture it, you get the expression!