What happens when the temperature of a liquid reaches its freezing point?
That's when the liquid goes into an equilibrium state, where:
#DeltaG_"frz" = 0 = DeltaH_"frz" - T_"frz"DeltaS_"frz"#
#-> color(blue)(DeltaH_"frz" = T_"frz"DeltaS_"frz")#
In this event, we are assuming a constant temperature and constant pressure (when a vessel is large enough, the pressure can be assumed constant), i.e. during a typical freezing event that doesn't involve manually decreasing the pressure.
At this point, the heat taken away from the liquid stops lowering its temperature for as long as the freezing process is occurring, because it's going towards performing the phase transition instead. When all of the liquid is frozen, the temperature can continue dropping again.
This happens such that the equality is maintained:
While the liquid is not yet fully frozen,
#DeltaS_"frz"#decreases (a decrease in disorder in the system as the solid is being formed).
As that happens,
#DeltaH_"frz"#also decreases (heat is released from the system as stronger intermolecular forces than previously there are binding the solid together; you spend heat energy to make stronger bonds).