A very long time ago, the philosopher Aristotle . . .

composed his treatise on Rhetoric to help truth and justice prevail over falsity, to show how persuasion and reason can be used to convince an audience and to refute unfair argument. 

In other words, he identified how rhetoric enabled people to express and identify truth over falsehood, to persuade and reason in order to bring a reader or audience to a particular point of view, and to debunk unfair arguments.

Rhetoric is defined as "the ancient art of argumentation and discourse." 

It is,

The study of effective speaking and writing. And the art of persuasion.

Also:

Discerning how language is working in others' or one's own writing and speaking, one must. . . divide form and content, what is being said and how this is said.

Put another way, writing (or speaking) for its own sake is not important, but how one communicates and the quality represented in that communication is what matters most. Because the English language is so diverse and can be so powerfully used (e.g., Thomas Paine's The Rights of Man), rhetoric is simply the ability to converse in the most effective way.

Informative statements provide information. Based upon Aristotle's model, it is the sharing of the truth. Information is based on facts. A newspaper article and books of research are examples of information-based writing. In both of these forms, information is shared. It is literal—that is, to be taken as the truth.

Explanatory statements explain or clarify ideas, concepts, processes, and so on. This is also the sharing of truthful information. Clarification can provide proof of the veracity of a literary work, a political statement, or a scientific report. Details are supplied in order to provide understanding and support the explanations given. This kind of statement or writing refutes false or ambiguous ideas, statements, and so on.

Persuasive statements are not as rigid in nature as the informative or explanatory statements. The purpose of persuasive writing is to convince the reader or listener to come to a purported conclusion based upon the writer's ability to influence the reader's or audience's opinion or viewpoint. However, remaining constant to Aristotle's model, persuasive statements or arguments should also (in a perfect world) reflect truth and a desire that justice prevail by using facts—information based upon truth rather than opinion. This is a difficult feat especially because sometimes partial truths or ill-informed information is used to make a persuasive statement or argument. Consider the editorial page of a newspaper where persuasive writing is employed, but overall acceptance of the factual nature of the piece is not guaranteed. 

All three basic forms are the structures used in all kinds of writing. Each kind of statement shares information that is helpful to the reader or audience in some way. The content of the statement and its intent are important regardless of the kind of statement used. In its truest form, these rhetorical statements should be used to enhance and elucidate ideas and share information with the reader: this is called content. Form is how the types of writing are presented, and good form allows the writing to be impactful (perhaps even memorable) in some way.

This is a way of classify statement types by purpose. It's not really a system used in contemporary rhetorical theory or scholarship, but rather just a pedagogical device. In other words, your teacher may be using this way of dividing up types of statement to help you think about how to compose a persuasive essay. The distinction between informatory and explanatory is probably based on the notion of simple statements you assume your audience will understand -- i.e. "the distance between New York and London is X miles". You would explain things you assume your hearer does not understand. Persuasive statements assume knowledge and understanding, and add an element of judgment and conviction.