This is off of owl.purdue.edu:
An analytical paper breaks down an issue or an idea into its component parts, evaluates the issue or idea, and presents this breakdown and evaluation to the audience.
Example of an analytical thesis statement:
An analysis of the college admission process reveals one challenge facing counselors: accepting students with high test scores or students with strong extracurricular backgrounds.
The paper that follows should:
Explain the analysis of the college admission process
Explain the challenge facing admissions counselors