In its simplest form heat is just molecules with energy moving around. The more energy you throw into the mix the faster the molecules move and the hotter something gets. Boiling water is just water molecules moving really really fast.
In a solid such as a metal when you heat it the particles start vibrating, not moving like the water molecules are but still moving at an atomic level. The fact that metal atoms are surrounded by a sea of electrons and the atoms are closely packed speeds up this process. This is why metals are good conductors.
If it is a solid – it transfers through conduction – hot atoms vibrate and transfer some of their heat energy to their neighbouring atoms.
If it is a liquid or gas, heat transfers through convection and conduction – atoms that are next to each other still transfer heat through conduction, but the hot liquid/gases move and mix with colder liquid/gases raising their average temperature as they do.
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