“Catch It On the Fly” refers to the (by 1867) near-total elimination among amateur clubs of the bound-out rule, under which a batter was called out if a fielder caught a fly on the first bounce in fair territory. One-hop catches in foul territory remained outs until the 1880s, but by the early 1860s it was increasingly considered unmanly to allow a ball fairly hit to bounce once instead of catching it before it touched the ground. The widely accepted Knickerbocker Rules codified the “fly catch” in 1864.

http://www.baseball-almanac.com/rulechng.shtml