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 through out the series run of Charmed as the three main characters (The Charmed Ones) are connected through The Power of Three. This type of magic is said to be the strongest that has ever, does and will exist. The Triquetra is The Charmed Ones symbol of their Power of Three.

Evil beings have also been seen to exploit The Power of Three. For example, the Rowe Coven were a trio of two warlocks and a half warlock (just like the reconstituted Charmed Ones) who, when their circle was complete, would invoke The Power of Three. The Triad also have The Power of Three.

Pros & Cons
The effect of a Power of Three bond being formed is that all the members' powers are pooled together into a Collective. The advantage of this is that all of the member get a massive general power boost due to each of the have effectively three times the amount of power they had before due to each being able to access their own as well as the other two's powers, rasing lower leves beings to high ones.

Of course, the downsides of this are that the amount of power one gains from this is relative to the level of the other beings involved, with the above example assuming that the beings involved are (at least more or less) the same strength.

Another downside of this is that if one member dies it weakens the Collective, making the oher 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/affct 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 creatire instantly. The Triad are also highly resiliant to Piper's combustion power whereas other lower level demons usually disintergrate within seconds. Therefore this particular con is easily balanced out.

Then there is the fact that this collective interconnects all of the members to each other in various metaphysical ways. Certain spells cast on one memeber may affect the others through this interconnection such as when Prue was magically turned evil, causing Piper and Phoebe to turn evil also.

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 eachother, emotionally or sokething 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.

Another way, mentioned above, would be if one of the members died. Althogh this event is less likely the implications are more severe as there isn't really a way of coming back from that one except under special circumstances.

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 once mentioned that her and her sisters once took one to always remain friends.

It may also be that one needs the aid of a spell to craete such a bond. Phoebe herself bestowed used a spell to release the power of the Charmed ones, titled the "Dominus Triunus":

''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 Four
This is real Charmed-world term and was used by the Phoebe of an alternate Universe where the balance of power was shifted towards evil. The term described the collective powers of Paige, Phoebe and their evil counter parts from the alternate universe, and is shown to be at leats as strong if notmore so than a Power of Three. Had both the evil and good Pipers not been in labour there could have also been a Power of Six.

The Power of Five?
During an earlier episode in season 1 Prue used the Charm of Multiplicity to make two duplicates of herself. With all three Prues using their powers together they had their own version of the Power of Three and together with Phoebe and Piper it could have well been possible that they could have had a "Power of Five".