One of my faculty position applications requires me to write a student success statement. I'm unsure what such a document should contain. Is this similar to a teaching statement?
I would recommend e-mailing a contact in the department and asking them. I expect that the answer would be "It's just a teaching statement", although it could be different.
Another thing you might do is search the university's website for "Student Success" and try to get a sense of what particularly the university means by this buzzword. Keep in mind that this requirement was possibly imposed by higher administration, and the people reading and evaluating your application might or might not have high regard for the intent behind it.
Edit: (too late for OP, but perhaps still of interest) From what I can tell, when universities talk about "student success" they are usually talking about efforts to make sure that students don't fall through the cracks. So in a "student success statement" you might talk about how you've gone out of your way to help students who are struggling.
This would be a (vague) request for some sort of documentation of your students' meeting some (ill-specified?) goals either within your course itself or in subsequent coursework... With "success" being defined in who-knows-what way. Most people would have no serious way to "prove" that they'd "benefited their students",... even while, perhaps, being asked to prove that.
It is never clear to what extent such unlikedly-to-be-truly-documentable claims play a role in hiring and such. Higher [sic] administrators obviously will love such concepts, because they make good PR, while are so vague that they could be used as excuses for fairly capricious acts.
E.g., it may well be that the hiring department is simply required by the central administration to request such a thing, even while fully realizing the dubiousness of its sense. Would not be at all surprising.