Heat energy, also known as thermal energy or simply heat, is the result of the process of transferring energy from one particle to another through the the energy transfer process. This is usually done through direct transfer of the energy through kinetic contact or through radiated energy as in the case of the sun.
When describing heat energy in intensity the common physics measurement is the joule (J) or calorie. As energy is stored, processed or transferred heat is released from the process when energy escapes from a closed system. This can be experienced when a computer operates, for example, and energy is regularly used by the machine for its processes. As energy is transferred from one circuit to another a build-up of heat occurs, hence why cooling fans are required for most machines in order to dissipate radiated energy before it becomes too volatile.
By describing heat as a particular form of energy, though, this is somewhat misleading as heat itself is simply one form of pure energy. A fire, for example, will radiate significant amounts of heat as carbon atoms are burned to produce power, yet this does not mean that they are generating heat as a form of energy – instead energy is being radiated that is then transferred to the surrounding areas when the energy waves come in contact with it. The farther the energy waves have to travel the less energy they contain, therefore by coming too close to a fire you may be burned by absorbing too much energy while being far away may yield no benefit at all if the energy dissipates before reaching you.
Similarly, if you were to write with a pencil quickly on a piece of paper you may realize that the end of the pencil increases in heat due to the friction the writing is generating. This heat is a form of kinetic energy transfer between the pencil and the paper and will dissipate quickly depending on how much or how little energy is retained, yet the same concept applies to all friction based kinetic energy transfers, such as the classic case of rubbing two sticks quickly together to create fire.
Common natural sources of heat energy in our world around us are the sun, or solar thermal energy, the earth, or geothermal energy, as well as chemical reactions that occur within all living organisms that generate chemical energy in addition to basic friction energy transfers.
Chemical energy being released by cellular reactions is the cause of many different experiences for living organisms and can be tied to a number of different organic functions, including the generating and maintaining of our own body temperature. This can best be experienced if you ever fall ill with a cold or the flu and develop a fever which is the result of increased chemical reactions within your own body as your body actively fights off invading organisms, or after a long run where your body temperature is raised significantly due to the increased metabolization of molecules needed to cause your body to move and function at an increased rate.