Once upon a time (300 years ago) in a billiard room far, far away…there were pool cues and CHALK!!!
Such an unassuming part of the game! Chalk is just a heap of granules formed into a cube, but it is as important as a well-playing table or a straight cue. Chalk is needed to keep the semi-curved cue tip from sliding of the oh-so-very-round cue ball.
Throughout most of the 1800's, when tips were made exclusively out of leather, the chalk used on leather cue tips was carbonate of lime, better known as blackboard chalk. Most chalk used today is comprised of fine abrasives and does not contain a speck of chalk.
Friction is the educated answer to the question, "why must pool players use a chalky substance to play the game well." A cue tip must cause friction on the cue ball to grab the surface and prevent a miscue.
It may seem a bit unlikely that something so outwardly minor could actually supply a fundamental force of physics such as this, but the surface roughness made by applying the chalk affects the sliding friction and the "motion-resistance" between the pool cue and the contact area on the cue ball. Ultimately, it prevents the players from a miscue, typically a faulty contact where the tip slides off the ball without the proper spread for the stroke.
As you contact the cue ball with your pool cue, the surface of the cue tip tends to get smooth and slippery. As an example, look at a pool cue tip that has been used for a number of shots, and a certain sheen will begin to be visible. This is a sign that the tip has basically compressed from taking a number of shots. The application of billiard chalk reduces the smoothness and allows the proper amount of friction between the pool cue and the cue ball.