Answer by taking a quote from the following article:

Thomas Andrews Hendricks (September 7, 1819 - November 25, 1885) was an American politician and lawyer from Indiana who served as the 16th Governor of Indiana (1873-77) and the 21st Vice President of the United States (1885). Hendricks represented Indiana in the U.S. House of Representatives (1851-55) and the U.S. Senate (1863-69). He also represented Shelby County, Indiana, in the Indiana General Assembly (1848-50) and as a delegate to the 1851 Indiana constitutional convention. In addition, Hendricks served as commissioner of the General Land Office (1855-59).

In 1872 Hendricks was elected as the governor of Indiana in his third bid for the office. An indication of Hendricks's growing national popularity occurred during the presidential election of 1872; the Democrats nominated Horace Greeley, the Liberal Republican candidate. Greeley died soon after the election, but before the Electoral College cast its ballots; 42 of 63 Democratic electors previously pledged to Greeley voted for Hendricks.  Hendricks served as governor of Indiana from January 13, 1873 to January 8, 1877, a difficult period of post-war economic depression following the financial Panic of 1873. Indiana experienced high unemployment, business failures, labor strikes, and falling farm prices. Hendricks twice called out the state militia to end workers' strikes, one by miners in Clay County, and one by railroad workers' in Logansport.  Although Hendricks succeeded in encouraging legislation enacting election and judiciary reform, the Republican-controlled legislature prevented him from achieving many of his other legislative goals. In 1873 Hendricks signed the Baxter bill, a controversial piece of temperance legislation that established a strict form of local option, even though he personally had favored a licensing law. Hendricks signed the legislation because he thought the bill was constitutional and reflected the majority view of the Indiana General Assembly and the will of Indiana's citizens. The law proved to be unenforceable and was repealed in 1875; it was replaced by a licensing system that Hendricks had preferred.  One of Hendricks's lasting legacies during his tenure as governor began with discussion to fund construction of a new Indiana Statehouse. The existing structure, which had been in use since 1835, had become too small, forcing the growing state government to rent additional buildings around Indianapolis. Besides its size, the dilapidated capitol building was in need of major repair. The roof in the Hall of Representatives had collapsed in 1867 and public inspectors condemned the building in 1873. The cornerstone for the present-day state capital building was laid in 1880, after Hendricks left office, and he delivered the keynote speech at the ceremony. The new statehouse was completed eight years later and remains in use as Indiana's state capitol building.

What did he do as Govenor?
One of Hendricks's lasting legacies during his tenure as governor began with discussion to fund construction of a new Indiana Statehouse.