The word for a bold independent thinker comes from a man who was simply not very good at ranching.
Samuel A. Maverick lived from 1803 to 1870. He signed the Texas Declaration of Independence in March 1836. He had studied law, but according to the Alamo, he made his career in business and land speculation instead. The Alamo notes his indifference to branding his cattle.
He got them almost by accident. The Handbook of Texas says that in February 1847 he bought a farm on the Matagorda Peninsula from Charles Tilton. The purchase included about 400 head of longhorn cattle. Merriam-Webster puts the number at about 450. The Handbook reports that their care fell to Jack, an enslaved man of nineteen, who asked for help that never came.
Few of the calves were branded. They wandered up the peninsula and onto the Texas mainland. In 1854 Maverick moved the shrunken herd, about 250 head, to a ranch in Karnes County. In 1856 he sold them to a neighbor, Augustine Toutant-Beauregard.
That sale is what spread the word, according to the Handbook. The deal required the buyer to round up the cattle himself. Toutant-Beauregard sent cowboys into nearby counties to collect every unbranded animal they could find, declaring each one a Maverick. The name began showing up in newspapers.
Dictionaries date the word to the late 1860s: 1866 in Merriam-Webster, 1867 in Etymonline. An 1885 Colorado statute defined a maverick as stock running at large "without a mother" and with "neither mark nor brand." In 1872 a dictionary of Americanisms linked the word to Samuel Maverick by name.
The jump from cattle to people came quickly. Etymonline records the sense of an "individualist" by 1886. The image is easy to see: a maverick is someone who carries no owner's brand.
The family kept the word alive in the 20th century. Etymonline credits Maury Maverick, Samuel's grandson, with much of its modern popularity. He was an independent-minded congressman from Texas. Etymonline also credits him with coining another lasting word, gobbledygook, in 1944.