How is "continuous wiring" defined in context of the 2017 NEC code?
Nope.  Nope nope nope.

You cannot use 210.12(A)(4) to put AFCI at an outlet.

There are certain fairly rare cases where you can put AFCI at the first outlet. 

However, there is a misconception that has turned into a regular "old wives' tale", that one can skip the expensive AFCI breaker and just slap an ACFI recep at the first outlet.  Oh no you can't! 

Of course, now that it's turned into a wives' tale, everybody is running for the Codebook hellbound to find the supporting language.  The closest thing they find to support their preconceived notion is 210.12(A)(4). "That must be it!" they say.  And they stick a Post-It there ready to throw it in the inspector's face. 

That wishful reading is possible if you totally ignore (4)(d): "blah blah system combination-type AFCI blah blah".  Go ogle that. That is a "married pair" of receptacle head-unit and trick breaker, both designed and UL-listed to work with each other.  The section was added to Code at Cutler Hammer's request, to support exactly one product, their SCAF20. 

Its killer feature is it uses Cutler Hammer's remote control breaker tech to allow resetting the breaker from the outlet. The outlet is just a "head unit" that controls the breaker.  So the guest can do it from the hotel room without calling the front desk.  Get it? 

Now go back and re-read 210.12(A)(4). See how it was written for the SCAF20?  Bingo.  It is not applicable to general AFCI outlets at all.

Other than that, Mrs. Lincoln, how about your original question? 

Continuous means no splices.

A solid run of NM-B or whatever you're rolling.  No Tyco in-wall splices. No stopping at an intermediate junction box.  No feeding some lighting circuits. Note that options (1) through (4) require a breaker which actually is an AFCI breaker.  (5) through (6) don't, but they require conduit, and there's already a rule against splices in conduit. 

Keep in mind that despite the name, AFCI is not anything like GFCI.  AFCI is mainly there to protect wires in the walls.  You can't put it at the first receptacle because that would leave the home-run totally unprotected.  That's only allowed in metal or concrete shelled conduit.