When the sugar crystals are dissolving at exactly the same rate that sugar is crystallizing out of solution, a system is at equilibrium. The balance between dissolution and crystallization can be changed by changing the temperature of the solution. Adding heat will favor dissolution. Cooling the solution will favor crystallization.
The temperature dependence of solubility is usually explained using Le Chatelier's principle. The principle states that when a system at equilibrium is placed under stress, the equilibrium will shift in a way that relieves that stress. In this case, the "stress" is the addition of heat. Le Chatelier's principle predicts that heating the solution mixture will shift the equilibrium in favor of dissolution, to remove the added heat. This explains why sugar is more soluble in hot water than in cold.
The temperature dependence of solubility is usually explained using Le Chatelier's principle. The principle states that when a system at equilibrium is placed under stress, the equilibrium will shift in a way that relieves that stress. In this case, the "stress" is the addition of heat. Le Chatelier's principle predicts that heating the solution mixture will shift the equilibrium in favor of dissolution, to remove the added heat. This explains why sugar is more soluble in hot water than in cold.