When you are "in line" to succeed someone, you are part of a line of succession determining who, and in what order, will replace a leader if he/ she cannot continue to serve due to death, disability or other causes.
Bad Example: U.S. Vice-President Joe Biden has apparently stated, incorrectly, "I'm second in line to be President!" If this was true, someone else would be first in line to succeed President Obama should any misfortune befall him. This is not correct.
Good Example: The Vice-President is first in line to succeed the President. The second in line is the Speaker of the House of Representatives.
Incidentally, a "Bidenism" is an incorrect statement made in a moment of loose mental concentration by Vice-President (and former Senator) Joe Biden. VP Biden has a history of statements that veer off in unexpected and unplanned directions.