Meaning 1
There are 9 innings in an American baseball game. A game will go into overtime when there is a tie, for instance 2 to 2.
Sentence 1
The Yankees won the ball game in the 9th inning, 5 to 2 runs.
Meaning 2
Part of a ballgame, whether baseball or in business or pleasure.
Sentence 2
"It is now the President's inning, and he has the masses of people behind him." (From "The Bully Pulpit," a book by Doris Kearns Goodwin about President Theodore Roosevelt.