Since 1956, back when Eisenhower was the president, the party that held the White House has traditionally gone second, so this year the Democrats have their convention after the Republicans.
During the years 1864 to 1956, the Democrats had their convention after the Republicans, with the one exception of 1888 when the Democrats went first.
There is no mention of conventions in the Constitution, and conventions have evolved over the years, along with the process of selecting nominees. The first nominating convention in American history occurred in 1831, when the anti-Masonic Party held their convention in Baltimore. The Democrats and National Republicans followed with conventions in 1832.