Understand and explain yourself: Make it interesting, insightful, revealing; how is your story different? Make it personal; possibly include information rarely shared with others. Be analytical; assess your life and experiences more critically than usual. Make it memorable; add drama (if appropriate) in the form of obstacles or challenges.
Who you are: More about your background and experiences than appears elsewhere in your application. What makes you tick? How are you different from other applicants?
Exposure to the field, accomplishments, experience: Through paid or volunteer work, research, classes, seminars, etc.
Why this particular school/program: The admissions committee wants to know that you did not apply randomly, but did your research and made an intelligent choice. Include information any specific faculty you'd like to work with and why.
Your academic and career goals: For most essays, you will be asked about these goals. Even if you are not 100% sure, give them an idea of potential careers and what you want to pursue in graduate school, and include specific faculty that you want to study with and why.
What Not to Include
Activities and jobs from high school (or before): In a graduate school essay, these often sound juvenile.
Editorial commentary: For example, "Lawyers should be . . ."
Divisive commentary: Be aware and judicious when you talk about areas of potential controversy, e.g., religion, politics, personal information.
Complaints: Don't whine. Address a deficit with a positive spin in terms of the effective resolution, learning and growth, resiliency, etc.