When tempering chocolates, we want that the chocolate will only contain beta crystals, for this, we melt the chocolate to a point where all crystals break, then cool it down to below the melting point of beta crystals, and then warm it back up to working temperature, which is just below the melting point of beta crystals. In many sources the lowers temperature to get to is 27°C, see for example this video by Callebaut Chocolate.
According to the Tempering section in the chocolate Wikipedia page, there are 6 types of crystals:
Crystal | Melting temp. | Notes
--------+-----------------+-------------------------------------
I | 17 °C (63 °F) | Soft, crumbly, melts too easily
II | 21 °C (70 °F) | Soft, crumbly, melts too easily
III | 26 °C (79 °F) | Firm, poor snap, melts too easily
IV | 28 °C (82 °F) | Firm, good snap, melts too easily
V | 34 °C (93 °F) | Glossy, firm, best snap, melts near body temperature (37 °C)
VI | 36 °C (97 °F) | Hard, takes weeks to form
Where it's obvious that we want only crystals of type V, but lowering the temperature to 27 °C, just below the melting point of the type IV crystals, allows them to be formed, before they are broken in the reheating.
Why do we allow chocolate to go below 28°C and allow type IV crystals to form, and not stop the process at 29°C?