What are thermal fluctuations?

[Trollfaz]

I often think thermal fluctuations as random changes in the temperature but when it is said in the context "thermally fluctuate over the energy barrier" does it mean to classically overcome the barrier?

 

[Drakkith]

I believe it usually means that something has been given enough energy to overcome a barrier via the random collisions in a collection of particles, such as the evaporation of water when it is far below its boiling point. Some water molecules are given enough energy to overcome the attraction of the surface molecules and escape into the air. They get this energy by colliding with a number of other water molecules such that enough energy is given to them to overcome the barrier.