A resistor in a circuit becomes very hot and starts to burn. This is because the resistor is dissipating too much:

When current flows through a resistor, it encounters resistance, which causes some of the electrical energy to be converted into heat. The rate at which this energy is converted and released is called power dissipation, which is measured in watts. Every resistor is manufactured with a specific power rating, such as 1/4 watt or 1/2 watt. If the electrical power in the circuit exceeds this physical rating, the resistor cannot shed the heat fast enough. This causes it to overheat, discolor, and eventually burn up. While excess current or voltage is what mathematically leads to excess power, resistors specifically dissipate this energy as power (heat). Therefore, burning is a direct result of dissipating too much power.