"The natural order hypothesis...states that, in general certain structures tend to be acquired early and to be acquired late." 
The Natural Order Hypothesis is one of the most difficult to accept for those who have done a large amount of Language Learning. Essentially it is saying that for each language, there is a generally predictable order in which grammatical structures will be acquired (not learnt, remember hypothesis 1). This order is a natural order, and so it does not normally correspond to the incremental grammar that typifies most courses of language instruction.
Krashen says that the research confirms natural order for children learning a 1st language, children learning a 2nd language, and adults learning a 2nd language. To the extent that that research is correct (it's well beyond my competency in the field), that is pervasive.
Remember, this is about acquisition. So a grammar test is not the kind of test that shows what has been acquired (see hypothesis 3). Rather, this order shows up when you do communicative tests and see what the learner uses naturally and what they understand but don't use and what they don't understand.
The hypothesis is not saying that this order is invariable for language students. There will be both individual variation among students, as well as variation based on what structures are regularly used in the acquisition environments.
The Natural Order hypothesis presents a real difficulty for classical languages. There is no real way to conduct the research needed to see what structures of Latin are acquired early or late. However, a recognition of this insurmountable (for the foreseeable future) difficulty could lead to a more ready acceptance of the alternative.
Krashen argues that instead of structuring the syllabus around incremental grammar, one should simply structure it around topics of conversation and communication. Especially things of immediate or everyday importance. This engages higher levels of interest (hypothesis 5) in the students, rather than a self-conscious focus on the grammar (hypothesis 3).
The Natural Order hypothesis flies in the face of most structured grammar courses, whether Grammar-Translation or Inductive-Reading. It's implications are difficult to accept, especially for classical languages, and it may be simply that we are not in a position to utilise this knowledge for language acquisition as effectively as we might hope.
 Krashen, S & Terrell, T. The natural approach : language acquisition in the classroom Oxford [Oxfordshire] ; New York : Pergamon Press ; San Francisco : Alemany Press, 1983.