The nut is the piece of plastic (in this instance) at the headstock end of the neck with the notches in that the strings sit in.
The flat side facing the fretboard is the face to measure from when checking scale length. The scale length is defined as twice the distance from the nut to the middle/crown of the 12th fret. So if this distance is 17", the scale length = 2 x 17" = 34".
Because of the way strings vibrate, there is a small 'dead' section at each end of the string that doesn't vibrate, and the thicker the string, the longer this section is. This is why the distance from the nut to the saddles with the guitar fully intonated, will always be a bit longer than the nominal scale length, and why the bottom E saddle will be further away from the nut than the G string saddle will be.
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