The idea that electricity flows from the positive terminal to the negative goes all the way back to one of America's Founding Fathers, Benjamin Franklin. In Ben Franklin's time, there were no batteries, and no knowledge of the existence of electrons. He discovered that when certain hard, smooth substances were rubbed against cloth-like fibrous surfaces, an attractive force was created between the two.
If the bodies were brought close to each other, the attractive force would discharge between them as a spark. Franklin imagined that a special kind of fluid called "electric fluid" existed in the bodies, and would move from one body to another when they were rubbed together.
In order to record his experiments for posterity he needed to give names to the new ideas and objects he was dealing with. He imagined that the hard and shiny things - glass, wax, amber and sulfur - had more electric fluid than the materials with fibers on the surface - wool, dry cloth, or fur. He concluded that the electric fluid moved from a place of plenty (he called it "positive") to a place of deficit ("negative"). After Ben Franklin wrote about this idea in 1750, everyone adopted it because he was a respected pioneer in the field.
People continued applying Franklin's convention about electricity flowing from positive to negative even after batteries were invented, because there was no reason to challenge that view.
J.J. Thomson discovered electrons in 1897 to great fanfare. Right after that, it became obvious that rather than positively charged particles going from positive to negative, the reverse was true! It was the negatively charged electrons moving from negative to positive, that we experienced as "electricity". By 1897 however, Franklin's convention had been in use for nearly 150 years, so appeared in thousands of books, tens of thousands of electrical circuit diagrams, and millions of minds by then.
Although Franklin's convention is not true in the context of conducting metals, it continues to be used in textbooks and circuits showing conducting metals (i.e., wires). Interestingly however, there are some cases of electric flow in which his convention holds true! When electricity flows through conducting fluids (electrolytes), positively charged particles (ions) flow from positive to negative, thereby matching the direction of conventional flow as imagined by Ben Franklin. There are a few other cases where the conventional direction is actually matched by the flow of postively charged particles.
As a concession to tradition, we refer to the direction of current that Franklin imagined as "conventional flow". Scientists are now in agreement that in metals, electrons flow from negative to positive and produce electricity (nothing actually flows from positive to negative).