I make it my goal to explain these things, in the spirit of my main teacher, Rabbi Manis Friedman, in a way that is non technical and can be understood in every day language.
In life, there are many things that are exciting and powerful, but not good. Anger is a good example to work with for this. Anger is one of those aspects of life and creation that contains an energy, a passion, that itself is not bad. However, that energy and passion belong to anger, which is bad (exceptions not included).
The evil and bad are going to be gone forever when Moshiach comes. Our goal, before that happens, is to rescue those energies and passions that are currently in the hands of the "dark side" and bring them over to the good side.
Given that there are so many different "sparks", and each has its own character and method, it's hard to cover all bases, but I will give a couple of examples:
When it comes to anger, this is one way in which we rescue its spark. Imagine a husband and wife who love each-other to the maximum degree their hearts can love. Then they have a fight, and a lot of anger comes out. When they deal with that, and make up, they love each-other more; more powerfully, more passionately, than they did before the fight! Where did this extra love come from? It came from the passion and energy of the anger. It has been rescued from that bad force and brought to a good purpose, just like Hashem wants!
Another example is Hitler yemach shemo. He was very evil, no question. Yet there was an energy in his evil, let's call it "insanity", that itself, is not specific to evil. He was insanely evil. Who is insanely good to match Hitler? Whoever is has rescued some very powerful spark...
We live in a world where evil gets all the sparks, unfortunately. The manifestation of this is that doing good is dull, boring, takes effort. Evil on the other hand is exciting, powerful, and has a lot of momentum and draw that good simply does not have.
This is a result of the Kabbalistic concept of the vessels having been shattered. The normal is that good should have this type of draw, energy, momentum and excitement and evil should be dull, boring and stupid. By rescuing sparks, which is predominantly achieved through resisting temptation, and teshuva, we bring those sparks back to the good side and when the Moshiach comes we will have a world where good truly has won, and has defeated evil utterly and completely, and good itself is enhanced by this and we can enjoy the reward of that for eternity.
I have based this, as mentioned on Rabbi Manis Friedman's explanations because he is an expert in both the technical chassidus and the art of translating it into every day understanding. This shiur in particular covers these points. The other answers have brought good sefarim that deal with these ideas in the original.