A synthesis essay begins with an examination of different "texts." The word "texts" here might mean stories, novels, poetry, or articles from a journal or magazine. Quite often the different texts might have opposing points of view or very different ideas. The point of a synthesis essay is to reconcile the different texts in a way that they can be understood to work together. Sometimes a synthesis essay also includes a more personal element, a discussion by the writer of why these particular texts are seen to be consistent by the writer.
An example of the kinds of texts that might be used in a synthesis essay might be an article about why Heart of Darkness is a racist novel and an article discussing why Heart of Darkness is not a racist novel. Depending on how each author supports his or her point of view, it is possible to synthesize both articles by writing about why both points of view are correct or have something in common.
Your professor might have very specific requirements for this form, but generally, you will need an introduction stating a thesis that represents the synthesis you perform, summaries of both texts, summaries that include the details you will need to reconcile them, and a section in which you synthesize the disparate elements of the texts.