Rachamim means compassion. But the translation of the word is only a small part of the meaning.
First of all, the word appears to be in the plural form. However, like the various names of God that have plural form, there is no sense of multiplicity in the word -- just majesty. The concept of compassion being among the most majestic of qualities is conveyed by its grammatical form.
The singular form of the word is "rechem," and it means "womb." Hebrew understands the function of the womb to be identical with the nature of genuine compassion. A woman who nurtures a life in formation makes room within herself and provides from her very essence to sustain that life. Compassion is the same kind of selfless nurture, but in the wider world.
When we attribute rachamim to God -- as we do in many circumstances --we are affirming the profoundly feminine aspects of God's presence, hosting us, as it were, within the divine essence. And in the context of this phrase, "giving life to the dead with great compassion," we present an image of God who takes the dead within and nurtures them with the divine self to bring them to life.
The image is fertile and provocative, but gives us reason to see an example of loving and nurturing behavior whenever we contemplate the nature of the human being -- who we are and how we each came to be. It also enables us to see God and God's attributes in the context of the selflessness that brought us to life.