Noun

1. The basic, central, or essential point or feature.

   The crux of her argument was that the roadways needed repair before anything else could be accomplished.

2. The critical or transitional moment or issue, a turning point.
   • 1993, Laurence M. Porter, "Real Dreams, Literary Dreams, and the Fantastic in Literature", pages 32-47 in Carol Schreier Rupprecht (ed.) The Dream and the Text: Essays on Literature and Language.

     The mad certitude of the ogre, Abel Tiffauges, that he stands at the crux of history and that he will be able to raise Prussia "to a higher power" (p. 180), contrasts sharply with the anxiety and doubt attendant upon most modern literary dreams.

3. A puzzle or difficulty.
4. The hardest point of a climb.
   • 1973, Pat Armstrong, "Klondike Fever: Seventy Years Too Late", in Backpacker, Autumn 1973, page 84:

     The final half-mile was the crux of the climb.

   • 2004, Craig Luebben, Rock Climbing: Mastering Basic Skills, The Mountaineers Books, ISBN 9780898867435, page 179:

     Most pitches have a distinct crux, or tough spot; some have multiple cruxes. ¶ Climb efficiently on the "cruiser" sections to stay fresh for the cruxes.

   • 2009, R. J. Secor, The High Sierra: Peaks, Passes, and Trails, Third Edition, The Mountaineers Books, ISBN 9780898869712, page 51:

     Continue climbing the groove; the crux is passing some vegetation on the second pitch.

5. A cross on a coat of arms.