It’s an adverb, “freshly” and we have a new “a-” to add to our understanding.  “A-” prefix 4 is a reduced form of “of-” prefix, indicating “of, from, off, or away”.  I suggest in this case it is “of” as in “of freshness”.

• 01.059 and set out everything afresh.

“a-, prefix4.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.

“afresh, adv.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.