Thermal energy, also called heat, is the energy that an object or system has because of the motions of its molecules. (So, thermal energy is really just kinetic energy at the microscopic level.) Thermal energy also involves some electromagnetic potential energy, because fast-moving molecules slam into each other harder than slow-moving ones, resulting in stronger electromagnetic forces pushing them apart again.
Heat is not the same as temperature. The heat a system contains is the total energy that it has because of the motions of its molecules; whereas temperature is (roughly) the average energy of the molecules. Technically this definition of temperature is only true for ideal gases, but it’s close enough to the correct definition for our purposes.
Since heat is a form of energy, it can be measured in joules. However, heat is often measured in calories. A calorie is the amount of energy needed to raise the temperature of a gram of water by 1 °C. Food calories are actually kilocalories—the amount of energy needed to raise a kilogram of water by 1 °C.
Temperature can be measured using various scales (e.g. Fahrenheit or Celsius), as I’m sure you already know. In science, the most commonly used temperature scales are the Celsius scale (historically called “Centigrade”) and the Kelvin scale. Degrees Celsius are symbolized °C. Increments on the Kelvin scale are not called degrees; they are just called kelvins and are symbolized with an uppercase K.
The coldest possible temperature is absolute zero, the temperature at which molecules aren’t moving at all. That temperature is 0 K (zero kelvins), or -273.15 °C.
Since heat is the total energy of the molecular motion, two gallons of boiling water have twice as much heat as one gallon of boiling water, even though the temperature is exactly the same in both cases (100 °C). Similarly, there is much more heat in a frozen lake than in a steaming teapot, simply because there are far more molecules bouncing around in the huge lake than in the little teapot (short and stout).
In this simulation, you can visualize how thermal energy (molecular motion) is manifested in different states of matter. Click the “States” experiment and try adjusting the temperature of neon, oxygen, argon, and water to see how the molecular motion changes as the substance transitions between solid, liquid, and gas states. In the “Phase Changes” experiment, you can also visualize how pressure plays a role in determining the state.