Simply put, it is a way to not only identify with the suffering of all other beings but to go a step farther and actually endeavor to take such suffering upon one's self in order to free others. Here is a description from Ken Wilber's book Grace and Grit:
And so where the Hinayana teachings stress individual enlightenment, the Mahayana teachings go one step further and also stress the enlightenment of all beings. It is thus the path, first and foremost, of compassion, and this is meant not just in a theoretical sense; there are acutal practices for developing compassion in your own mind and heart.
Foremost among these practices is the one known as tonglen , which means "taking and sending." After one has developed a strong foundation practice in vipassana, one moves on to the practice of tonglen. This practice is so powerful and so transformative it was kept largely secret until just recently in Tibet. And it was this practice that Treya took to heart. The practice is as follows:
In meditation, picture or visualize someone you know and love who is going through much suffering--an illness, a loss, depression, pain, anxiety, fear. As you breath in, imagine all of that person's suffering--in the form of dark, black, smokelike, tarlike, thick, and heavy clouds--entering your nostrils and traveling down into your heart. Hold that suffering in your heart. Then, on the outbreath, take all of your peace, freedom, health, goodness, and virtue, and send it out to the person in the form of healing, liberating light. Imagine that they take it all in, and feel completely free, released, and happy. Do that for several breaths. Then imagine the town that person is in, and, on the inbreath, take in all of the suffering of that town, and send back all of your health and happiness to everyone in it. Then do that for the entire state, then the entire country, the entire planet, the universe. You are taking in all the suffering of beings everywhere and sending them back health and happiness and virtue.
When people are first introduced to this practice, their reactions are usually strong, visceral, and negative. Mine were. Take that black tar into me? Are you kidding? What if I actually get sick? This is insane, dangerous! When Kalu first gave us these tonglen instructions, the practice of which occupied the middle portion of the retreat, a woman stood up in the audience of about one hundred people and said what virtually everybody there was thinking:
"But what if I am doing this with someone who is really sick, and I start to get that sickness myself?"
Without hesitating Kalu said, "You should think, Oh good! It's working!"
That was the entire point. It caught all of us "selfless Buddhists" with our egos hanging out. We would practice to get our own enlightenment, to reduce our own suffering, but take on the suffering of others, even in imagination? No way.
Tonglen is designed exactly to cut that egoic self-concern, self-promotion, and self-defense. It exchanges self for other, and thus it profoundly undercuts the subject/object dualism. It asks us to undermine the self/other dualism at exactly the point we are most afraid: getting hurt ourselves. Not just talking about having compassion for others' suffering, but being willing to take it into our own heart and realease them in exchange. This is true compassion, the path of the Mahayana. In a sense it is the Buddhist equivalent of what Christ did: be willing to take on the sins of the world, and thus transform them (and you).....A strange thing begins to happen when one practices tonglen for any length of time. First of all, nobody actually gets sick. I know of no bona fide cases of anyone getting ill because of tonglen, although a lot of us have used that fear as an excuse not to practice it. Rather, you find that you stop recoiling in the face of suffering, both yours and others'. You stop running from pain, and instead find that you can begin to transform it by simply being willing to take it into yourself and then release it. The real changes start to happen in you, by the simple willingness to get your ego-protecting tendencies out of the way.....A great "equality consciousness" develops, which undercuts pride and arrogance on the one hand, and fear and envy on the other.
When I was learning about tonglen I had an office mate who was absolutely horrified that I would practice it. She thought I would drop dead or something, given my health problems. (I figured what the heck, if I'm likely to die young anyway may as well accomplish something useful.) Her worry was for naught; I've never been harmed by tonglen. Or maybe I just haven't perfected it yet. :)