Technically, if we’re going to talk about the yetzer hara, we’ll also discuss the yetzer hatov.
Rabbis in a little shtetle (village) in Poland decided to trap the yetzer hara so that it would stop tormenting the Jews of the town. Somehow, they did it. They trapped the yetzer hara in a wardrobe (like a boggart in Harry Potter). A few months later, the rabbis were distraught and began discussing the need to release the yetzer hara. Once it was trapped, the villagers lost the motivation to go to work, to have children, to create art, etc. They decided to release it back into the world.
All of those acts (for the average person, not some tzaddik) require some degree of selfishness, which is primarily what the yetzer hara does. It makes you think of yourself instead of Hashem or others.
This was stated more eloquently in The 6 Constant Mitzvos:
The yetzer hara‘s sole purpose for existence is not to distract us from serving Hashem, but to help us grow. His entire existence is one of illusion. His role is that of a coach, who pushes an athlete to the extreme to help him attain success. When he says, “Sin,” he really means, “Let me see you withstand my challenge and become great.”
The yetzer hara may seem like a nuisance, but he sells the tickets to eternal pleasure. You cannot grow without him. You cannot perfect yourself without being challenged by increasingly difficult circumstances.
In other words, the yetzer hara and the yetzer hatov have the same goal: help you grow and serve Hashem. Yin and yang, if you will. (Full disclosure: I know essentially nothing about yin and yang, so I hope that superficial comparison actually works as an analogy.) Put in lawyerspeak… good cop, bad cop.
And that last sentence is why people often say that tzaddikim have the strongest yetzer haras. They might as well be saying, “That rabbi can bench press 800 pounds!” Because tzaddikim have successfully survived the yetzer hara’s challenges, each challenge from the yetzer hara is harder than the one before. Gd willing, that should be the case with all of us! This is the proof that you have grown and aren’t stagnating in your faith or observance.
Just as a note… the story about the Rabbis in Poland never happened.
I know this for two reasons.
First, all such stories are made up. There were never even any Rabbis in Poland (and I write this as the great grandson of a Rabbi in Poland).
Second, the story is actually a medrash from Bereishis Rabbah (9:7); the Soncino translates it as "7. Nahman said in R. Samuel's name: BEHOLD, IT WAS VERY GOOD refers to the Good Desire ; AND BEHOLD, IT WAS VERY GOOD, to the Evil Desire. Can then the Evil Desire be very good? That would be extra- ordinary ! But for the Evil Desire, however, no man would build a house, take a wife and beget children ; and thus said Solomon : Again, I considered all labour and all excelling in work, that it is a man's rivalry with his neighbour (Eccl. IV, 4). 2 " [source http://www.archive.org/details/midrashrabbahgen027557mbp ]