thermal energy
Thermal energy is the total energy tied up in the ceaseless random jiggling of all the particles inside an object. Every atom in this page is vibrating a little; add up the energy of all that microscopic motion and you have the object's thermal energy. Heat something up and this jiggling grows more vigorous, so its thermal energy rises.
More precisely, thermal energy is the part of a system's internal energy that comes from the random motion of its particles. It is closely tied to temperature but is not the same thing: temperature is the average kinetic energy per particle, while thermal energy is the grand total over all the particles. That makes thermal energy extensive; it depends on how much material there is.
This distinction resolves a common puzzle. A cup of boiling water at 100 C is hotter than a bathtub of warm water at 40 C, yet the bathtub holds far more thermal energy, because it contains so many more molecules all contributing their share. Note too that 'thermal energy' is sometimes used loosely as a synonym for internal energy, though strictly internal energy can also include energy stored in molecular bonds.
An iceberg at -10 C is far colder than a mug of coffee at 60 C, yet the iceberg holds enormously more thermal energy, because it contains so vastly many more molecules.
Thermal energy depends on amount as well as temperature: bigger and colder can still mean more total energy.
Thermal energy (total, extensive) is not the same as temperature (average per particle, intensive), and it differs from heat, which is thermal energy in the act of transferring.