Initially, the games were part of other mid-winter civic celebrations (like the festival of Roses and what is now called the Rose Bowl Parade in Pasadena) in warmer climates, designed to get rich college alumni from the North to follow their teams to the games (Rose Bowl in Pasadena, Orange Bowl in Miami, Cotten Bowl in Dallas, or Sugar in New Orleans), escape the winter in Michigan, Minnesota, or other such places, and drop lots of money on the local economy.
More cities, like El Paso (Sun Bowl), Tampa (Tangerine) and Atlanta (Peach Bowl) followed, and college teams and fans started viewing the games as rewards for a good season, and a way of attracting new recruits.
Finally, the bowl games were seen as 1) essential for a team (nominally related to a college) to to feel important (and recruit), 2) necessary for the television networks to provide programming that produced big bucks from advertising rights, 3) an excuse for college presidents and other officials to go to warm climates to party and live it up at someone else's expense, and 4) the television revenue from the various (this year 32) bowl games is divvied up among the schools of the various conferences and totals in the hundreds of millions of dollars which support not only the multi-million dollar contracts of the coaches, lots of job positions at the colleges, and also underwrites all the sports required by Title IX that lose money and no one watches.