Heat travels in waves like other forms of energy, and can change the matter it touches. It can heat it up-which starts molecules moving or it can cause chemical reactions like burning to occur.
Heat can be released through a chemical reaction (such as the nuclear reactions that make the Sun "burn") or can be trapped for a limited time by insulators. It is often released along with other kinds of energy such as light, radio waves, or sound waves. A burning candle releases light and heat waves; an explosion releases light, heat, and sound waves. The Sun releases all kinds of energy waves.