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.
Informative- a literal statement wherein you just give data or information. From the word itself, 'to inform'--just a fact or your own opinion about a certain topic
Explanatory- higher level than informative because here, you need to give details to support the topic. you may describe or narrate anything related to the topic--'elaborate details'
Persuasive- the hardest of these three for you need to persuade others to believe and agree with your thoughts. Having this said, you need to support your statement with proofs or evidence so as to catch their interest and side.
***to sum it up, first you need factual statements for information (informative) afterwards, you need to elaborate those and give supporting details (explanatory) then finally, prove them to make your readers agree with you (persuasive)
#hope this helps. :)