Thermal energy is energy possessed by an object or system due to the movement of particles within the object or the system. Thermal energy is one of various types of energy, where 'energy' can be defined as 'the ability to do work.'
Work is the movement of an object due to an applied force. A system is simply a collection of objects within some boundary. Therefore, thermal energy can be described as the ability of something to do work due to the movement of its particles.
Because thermal energy is due to the movement of particles, it is a type of kinetic energy, which is the energy due to motion.
Thermal energy results in something having an internal temperature, and that temperature can be measured - for example, in degrees Celsius or Fahrenheit on a thermometer. The faster the particles move within an object or system, the higher the temperature that is recorded.
Let's take a look at a simple example of thermal energy. A heated element on a stove contains thermal energy, and the more you turn up the stove, the more internal energy the stove contains.
At the very basic level, this thermal energy is the movement of the molecules that make up the metal of the stove's element. I know you can't see the molecules moving, but they are. The faster the molecules, the more internal thermal energy they contain.
Now, let's place a pot of water on top of the heated element. What happens? The stove works, right? Well, not as we would typically think of it. Here, 'work' is referring to 'the movement of something when a force is applied.'
Specifically, the thermal energy of the stove causes the particles of the pot and eventually the water to move faster. The internal energy of the heated element is transferred to the pot and ultimately the water within the pot. This transfer of thermal energy from the stove to the pot and to the water is referred to as heat.
It is very important to keep these terms straight. In this context, heat is the term we use to refer specifically to the transfer of thermal energy from one object or a system to another, transfer being the key. The thermal energy is the energy possessed within the object or within the system due to movement of particles. They're different - heat and thermal energy.
You can feel the heat if you hold your hand above the stove. The heat, in turn, speeds up the molecules within the pot and the water. If you place a thermometer in the water, as the water heats up, you can watch the temperature rise. Again, an increase in internal energy will result in an increase in temperature.