When a company makes a profit, and has cash on hand, there are a few things they can do with that cash.

They could spend it to improve the company's operations. (buy better equipment, repair stuff, train staff, etc.) But people who buy and hold the company's stock as an investment generally don't like that, so companies don't do a lot of that.

The company could give all their employees raises. But the people who buy and hold the company's stock don't like that, because it doesn't make the stock price go up, and doesn't make them any money.

The company can issue some of its profits as a payment to the people who hold stock. This is called a dividend. This does make stock-holders more money, but dividends are taxable income, and the people who buy and hold stocks don't like to pay taxes.

The company can literally purchase some of its own stock off the stock market to take back. Buying stock creates demand, and reduces the supply of available stock that other people could buy, so that often results in the stock price increasing. People who buy and hold stocks like it when the value of their stocks increase, so they like this.

Stock buy-backs are very literally open attempts by the company to manipulate the stock price, and for a very long time, they weren't just frowned upon, but outright illegal.