In this line from Walt Whitman's poem <em>Song of Myself</em>, the meaning of the word <em>leavings</em> is <em>inheritance/legacy</em>.
Explanation:
The speaker expresses what he feels about the life of the other person; he feels his/her life is a consequence of many deaths, that maybe the way of living and the characteristics of that life are what they are because of that deaths, what those deaths left him/her. His/her inheritance/legacy made of his/her life what it is.
Explanation : As described in the above lines Heigl is trying to face her fears in public by speaking the feelings what she is experiencing within herself. She is building her confidence by openly expressing and facing the fears within her.