Thermal fluctuations refer to random changes in temperature that can lead to significant effects, such as particles overcoming energy barriers. In the context of thermally fluctuating over an energy barrier, it implies that particles gain sufficient energy to surpass the barrier through random collisions. For example, water molecules can evaporate at temperatures below boiling point by acquiring enough energy from collisions with other molecules. This process allows some molecules to break free from surface attraction and enter the air. Understanding thermal fluctuations is crucial in explaining phenomena like evaporation and other temperature-dependent behaviors.