A relay is an electrically operated switch. It consists of a set of input terminals for a single or multiple control signals, and a set of operating contact terminals. The switch may have any number of contacts in multiple contact forms, such as make contacts, break contacts, or combinations of them.
Relays in automotive use are almost always to switch large current devices like fans, fuel pumps, heads lights or anything that draws more current that what the switch used is capable of flowing. We use relays in the E9x swaps to control things like fuel pumps and ac compressor clutches.
The diagram below is of a basic 5 pin type automotive relay. Pin 30 is the incoming wire that gets switched between pin 87a and 87. In the normal state pin 30 is connected to pin 87a, when power and ground is connected to the coil (pins 85 and 86), pin 30 connects to pin 87.
So if you are trying to switch power to a fuel pump, you would wire 12v power to pin 30, and the power side of the pump to pin 87, and ground the other wire of the fuel pump. Now when we put power to the coil wires (pin 85 and 86) the relay will click, connecting power from pin 30 to 87, and power the pump.
Triggering the coil of the relay (pin 85 and 86) can be done in 2 ways, either switch the power or the ground side of the coil.
If you are triggering a relay with a 12v signal (like the green Holley fuel pump wire) you will use this diagram below.
If you are triggering a relay with a Holley IO output you will use this diagram below.