Heat is thermal energy, and in solids it can be transferred by conduction. Heat is passed along from the hotter end of an object to the cold end by the particles in the solid vibrating. The hotter particles vibrate a lot and cause the particles next to them to vibrate as they gain heat energy too.
Fluids, that is both gases and liquids, can transfer heat energy by convection. It is easiest to explain this while thinking of an example:
Imagine a beaker of water being heated from the bottom. As the water particles at the bottom get hot, they expand and become less dense.
Radiation is different to the other two processes as it doesn't require particles in its transfer of energy. Instead, infra-red radiation is a type of electromagnetic radiation. This means that the energy is transferred by waves rather than particles.
Radiation is how we feel the heat from the sun on Earth, as waves can pass through the vacuum of space where there are no particles.