A resistor obeys Ohm's law ($\small V=I\cdot R$); the current through it is equal to the voltage across it divided by the resistance (equivalently $I=\frac{V}{R}$).
A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's terminals to the intensity of current through the circuit is called resistance.
Resistors are often rated in ohms (resistance) and in watts. The watt rating of a resistor indicates how much power that resistor can safely dissipate continuously. This rating is very dependent on mechanical orientation and airflow.
Resistors also often have an overload spec, allowing the power rating to be exceeded for a specified time. This overload spec is largely dependent on the mechanical structure of the resistor. Wire-wound resistors are commonly rated for 10x for five seconds, while film resistors have much lower overload capability.
Some resistors are instead rated in joules, specifying the maximum energy the resistor can absorb. These are typically used for single-shot pulse applications, with long times between pulses.
Resistors can be through-hole (sometimes called radial), surface mount, or chassis mount. Specialized resistors include precision resistors (< 1% tolerance) and power resistors (from 1 W on up).
The resistance of a resistor changes with the temperature of the resistor. The temperature coefficient of a resistor is typically specified in PPM.