There were two main roots of the cattle boom after the Civil War.

On the demand side of the equation, there was the demand that was coming from the cities of the East.  The cities were growing and people were demanding more meat.

On the supply side, there were the railroads.  The railroads started to spread out into the Great Plains.  By doing so, they provided places where cattle could be brought (from Texas in particular) to be transported to the markets of the East.  The most famous of these was the town of Abilene, Kansas, which was essentially created by cattlemen as a place for ending cattle drives and putting the cattle on trains.

The boom, then, was driven by increasing demand from the growing cities in the East and by the expansion of railroads that made it possible to get cattle to that Eastern market.

What were the roots of the American cattle boom after the Civil War?

Longhorn cattle were introduced into the area that became the state of Texas by the Spanish who crossed the Rio Grande from Mexico.

Cattle have been raised in Texas from the time the Spanish attempted to establish missions and domesticate the Indians, beginning in the mid-18th century.

Because of the large areas of land suitable for open-range pasture, the number of cattle raised in Texas expanded as cattle drives supplied meat to the California goldfields and to military forts and Indian reservations in the southwestern territories during the 1850's.

After the Civil War, cattle drives resumed and expanded the territory through which they passed. Well-known trails such as the Chisholm and Goodnight-Loving trails supplied hundreds of thousands of head of cattle to markets or railheads, which arrived in Texas in the 1870's.