The Sharp Points sidebars give examples of features of the natural world that illustrate the fine tuning, purposeful design and planning that is invested in creation. The phrase comes from the theme of lectures delivered by Dr. Bossard: SHARP POINTS: God's Conspiracy to Evangelize the Inquiring Mind (1997). This is available here in html and audio.
A Sharp Point indicates the work of a Creator. The point can be resisted with effort, but the cumulative effect of many sharp points may lead (has led) some scientists to consider the reality of the Creator. A good example of these sharp points is the many "coincidences" that are wrapped up in the Anthropic Principle, and summarized very neatly by Fred Hoyle in the remark "I do not believe that any scientist who examined the evidence would fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce inside the stars. If this is so, then my apparently random quirks become part of a deep laid scheme."* That "deep laid scheme" implication captures the essential feature of a sharp point.
* Quoted in Barrow & Tipler, the Anthropic Cosmological Principle (1981) pg. 22, from a lecture by Fred Hoyle in Religion and the Scientists (SCM Press, 1959)