The functions that are executed are called Interrupt Service Routines (ISR) and are more or less simple functions, but that do not take arguments.
Let us see an example, something like counting some pulses. The ATMega328P has an Analog Comparator that has an interrupt associated that is activated when a signal surpasses a reference voltage. First of all you must define the function that will be exectuted:
This is really simple, the instruction ISR() is a macro that tells the compiler that the following function is an Interrupt Service Routine. While ANALOG_COMP_vect is called Interrupt Vector and it tells the compiler which interrupt is associated to that routine. In this case it is the Analog Comparator Interrupt. So everytime that the comparator sees a signal bigger than a reference it tells the microcontroller to execute that code, id est in this case to increment that variable.
The next step is to enable the interrupt associated. To enable it we must set the ACIE (Analog Comparator Interrupt Enable) bit of the ACSR (Analog Comparator Setting Register) register:
In the following site we can see the list of all Interrupt Vectors: