An "usher" is a person who guides people to their seats, in a theater or a church. He welcomes people at the door, perhaps takes them by the arm, and brings them in.
Figuratively, we can say that a statesman "ushers in" an era. It means he was one of a number of people who we think of as connected with the era, who were active at the start of the era, and influential in guiding the nation into the new era. He was active at the start of the era, just as an usher stands at the entrance, and he helped bring the nation into the new era, just as an usher helps bring people into the theater or church.
For example, in music, it is customary to talk of a "classical era" followed by a "romantic era." We can say "Beethoven ushered in the romantic era." He was not the only romantic composer. He was not the first romantic composer. But he was early. He was important. He was a trend-setter. When we think of the romantic era, we think of it as starting with Beethoven.