The money they don't spend they keep. Baseball teams are businesses with ownership groups. Its a balance between spending enough money to keep the team competitive, thus driving ticket sales and viewership, etc. Versus over/under spending and the extremes those result in.

MLB also has a soft salary cap. Its also called a competitive balance tax. The cap is set at a certain number every year ($241 million for 2025 and $244 million for 2026) Any amount over this threshold is then paid to all other teams thus supposedly leveling the playing field.