Last week's definition:
Leadership is the way in which an individual acts to influence others around them. There are limitless ways or styles in which a person can lead.
This week's definition:
Leadership is the way in which an individual acts to influence others around them to produce results. Effective leaders should be able to utilize different leadership styles in different situations.
Analysis of the differences:
Two things changed about my definition. First I added an emphasis on producing results because being a good leader means influencing the outputs of a group in a positive way. A person isn't a very effective leader if they are not able to influence people to produce results. Second, I more specifically stated the importance of knowing when to use certain leadership styles based on the Goleman and Daniel (2000) article, "Leadership that Gets Results."
Goleman, Daniel (2000). "Leadership that Gets Results." Harvard Business Review, 78(2), 78-90.

Very nicely done.
Grade: 10 out of 10
Clarity of the new definition: 2 points
Thoughtfulness of the analysis: 6 points
Grammar, spelling, and APA style: 2 points