The phrase “deep, acute curves” as used toward the end of a cornell.edu “Introduction to the Elements of Design” webpage, refers to curves or bends where the perimeter of the curve is large compared to the area the curve encloses or excludes. In the design that the text refers to, Saul Steinberg's “Cut-out Family”, the mother's narrow waist and her elaborate dress, hair and hat provide examples of deep curves in this sense. The man and the child, on the other hand, are portrayed with few deep curves.
Edit: In wiktionary, the adjective deep has a dozen senses shown. Which correspond most closely to its usage in the phrase deep curves? Literal senses like “A long way inside; situated far in or back”, or “Voluminous”, or “Having its bottom far down” may apply; but the figurative sense “To a significant, not superficial, extent” is perhaps more appropriate. As a practical matter, shallow curves (“Having little depth; significantly less deep than wide”) may be easier to recognize than deep curves, which we may then define as “not-shallow curves”.
Note, the definition I gave of deep acute curves as “curves or bends where the perimeter of the curve is large compared to the area the curve encloses or excludes” is related to definitions of high curvature as given in wikipedia's curvature article. The unit tangent vector T mentioned there (or the unit normal N) sweeps through more angular area per unit of time for a high-curvature curve than for a low-curvature curve.