What does Beatty claim happened to the books over the years?

Beatty says that society changed to favor more sports and group activities, which resulted in less time to think. This meant more cartoons and pictures in books, and more impatience. People were always in a hurry to go somewhere in their cars, not sit and read.
In addition, more population meant a greater diversity of population. This meant authors had to write to mass audiences and remove the controversy from their books. Further, people turned more to magazines which became, Beatty said, bland like "vanilla tapioca."
People voluntarily read fewer and fewer books as time passed, even before books were banned. As the population became less informed, the government decided that it was better for everyone—made for greater happiness—if the population conformed to the same ideas. To enforce happiness and prevent children and teens who were smart from being bullied and tormented, the government decided to ban books altogether. Too much thought, it decided, leads to conflict and social unrest. Firemen would serve society by ridding it of books. As Beatty says,

A book is a loaded gun in the house next door. Burn it. Take the shot from the weapon.

Beatty tells Montag that people's attention spans narrowed to such an extent that they could only read something that was quick and simple. This meant that books became much shorter and more condensed, making them incredibly boring in the process. Add to that the systematic censorship of written material by the state, and it's no wonder that the demand for reading matter declined sharply. Books were simply regarded by the authorities as too dangerous, too subversive. They made people think, gave them ideas, and what's more, they provided people with an insight into the truth. And in a political system built on lies, that's the most dangerous thing of all.
Beatty's explanation is important to the story as it provides us with some useful background information as to how this dystopian society came to develop such a hatred of books. It also serves as a salutary warning that a desire for quick and easy information can all too easily lead to our lacking the time and the patience necessary to enjoy reading. This is a particularly relevant warning in the age of the smartphone.