We've all seen in many MLP episodes Twilight, AJ, Pinkie, Rarity, Fluttershy, and Dash all channel their energy into the elements of harmony creating a rainbow spiral in the series or in the case of rainbow rocks it creates a giant alicorn spirit energy... 

First lets look at the mlp version then get to the EG version and yes btw before you ask it is a bit different but technically speaking the elements ARE there in EG. 

The elements work by channeling the power of the soul based a six energy formation the center point being the full energy of the other five connected at one point and also connecting the other five to it as well. 

I say six energy point because given that that it has been shown the elements of harmony in the past used different energies from the six of magic, kindness, generosity, laughter, loyalty,  and honesty in the past which means that the elements of harmony can very much go by many different forms and different types of harmony energies.  Thus, it can be assumed so long as whatever energy channeled by the six individuals are some form of harmonious energy it will work just the same. 

In other words whether it is kindness, courage, love, earth etc etc it matters not just so long as it is something that allows the channeling of harmony overall.

 Anyways, the elements themselves only act a natural amplifier for the energy that is already there in the individual using it and as such by itself cannot create any power by itself per say. So, if the individual has either a warped of negative energy then the element/ elements will not work properly as seen when Twilight attempted to use them with her friends in their "corrupt" statuses. 

The tree of harmony itself I'm not 100% sure on how it works exactly but I assume that the elements act much like its magical heart and that without them the tree simply becomes an ordinary tree. The harmony energy of the elements within the tree are the harmony of all harmony elements fused together.  So, yes they are more powerful within the tree than with the individuals using them as unless the given pony in question is an absolute master of all harmony energy/magic their ability to use the element is limited to what they are capable of. 

Moving on, let's look at what the elements do to the opposing force or "evil character" they hit. First it is important to understand that in terms of positive or negative magic the two energies can never co exist and the two will always conflict with each other until they are both exhausted or  until one overpowers the other one.  in the case of the elements their positive energy removes and replaces the negative energy of the individual's dark magical power. 

The ending result of which depends on the level of good to evil the dark magic user being hit by the rainbow blast actually is. Luna was not an evil power but was more a misguided and toxic energy than an actual evil so the result for her was that the elements cleansed her of all all those  that were not part of her true self removing all of that toxic energy out of her. 

if you used the elements against someone who was good say if you tried to use them against Princess Celestia it would very likely have a healing or regenerative effect on them since all you are doing is adding more positive energy to another positive. 

Alright, that is a basic for how it works in Equestria so we can move on to the discussion of EG.  The truth EG is that the elements of harmony existing and being used by their pony counterparts automatically gives access to those same elemental energies for their human counterparts and the reason for that is that BOTH human and pony are in fact the very same being.  Thus the harmony power the humanized version of the mane six use are just a more watered down version of the power in Equestria as it is still there just the connection to that element is much weaker and is being channeled more from a kind of higher self in some sense. 

The power they are calling from is the point of connection between their human self and their pony self. 

Cool and all but how on earth does any of this have anything to do with me as a person?  Well, while it may not be as magical and flashy the cartoonish elements are a great example of both how to protect yourself from your more toxic traits and how utilizing this with other family and friends can help as well. You may not have a magical artifact but you can focus on affirmations and choose what energy you create and grow for yourself like wise you can help your friends and family to do the same and if you only grow the positive then you leave no room for the negative to take root thus it will go away in time. 

Now, an important thing to note is that being positive does NOT mean having your head stuck in the clouds or being in denial about things happening to you  by any means it just means that instead of dwelling on teh issue at hand you are looking for the solution to your problem and taking charge of the situation to empower yourself.  your own soul becoming an element in a way.