The Power of Three

The Power of Three is the generic term for any collective of powers that consists of three magical beings. The Power of Three has been a strong theme throughout the series run of Charmed as the three main characters (The Charmed Ones) are connected through the Power of Three. This is said to be the strongest kind of magic that has ever, does and will exist. The Triquetra is the theme symbol of Charmed, representing specifically the Charmed Ones themselves and their Power of Three, which is marked on their Book of Shadows. While most of the spells written in the book require the Power of Three to take enough effect, it isn't always necessary for all three sisters to chant a spell together, only as long as they are all together at the same time. For example, Phoebe cast the Dominus Trinus to awaken their powers as the Charmed Ones; Piper has summoned the Power of Three to save Paige from an invading spirit; Paige summoned it to vanquish a Slime Demon.

The Power of Three is used often in the Halliwell/Warren family. There magics became so strong they eventually vanquished the source.

Pros and Cons
The effect of a Power of Three bond being formed is that all the members' powers are pooled together into a Collective, which gives them High Resistance.

A downside of this is that if one member dies it weakens the Collective, making the other members easier to kill off with the death of each member. However, on the flip side, more powerful (and hence higher level) beings are harder to kill/affect with ones powers than lower level ones i.e. Piper and the other various Charmed Ones have been shown to have taken direct hits from all kinds of attacks such as fire and energy balls and live many times over whereas such attacks would vanquish any other magical creature instantly. The Triad are also highly resilient to Piper's combustion power whereas other lower level demons usually disintegrate within seconds. Therefore this particular con is easily balanced out.

A Power of Three bond can be broken in several ways. If the members use their powers on each other in a negative manner or atmosphere then the bond will be broken. Fortunately, this may be reformed by all of the members reconnecting with each other emotionally or something to that effect. For example, when the Charmed Ones used their powers on each other during an argument it shattered their Power of Three. However, later on they all got over the argument and showed their solidarity as sisters (which is where their Power of Three comes from) and hence reformed it.

Origins
It is not explicitly stated how a Power of Three bond is formed but prophecy, lineage, identity and mutual trust seem to be key factors. It could be possible one must take a blood oath to always remain together or something of that nature as Phoebe mentioned that she and her sisters once took one to always remain friends.

It may be that one needs the aid of a spell to create such a bond. Phoebe read a spell to bestow the power of the Charmed Ones upon the sisters, titled "Dominus Trinus":
 * Hear now the words of the witches,
 * The secrets we hid in the night,
 * The oldest of Gods are invoked here,
 * The great work of Magic is sought
 * In this night and in this hour,
 * We call upon the Ancient Power
 * Bring your powers to we sisters three!
 * We want the power!
 * Give us the power!

The Power of Six
After the new prophecy of Piper's children Wyatt, Chris and Skye becoming the next Charmed Ones they combined their Power of Three with Piper, Pheobe and Paige's Power of Three to vanquish the even powerful Source of All Evil making the Power of Six.