In trying to unpack the familiar phrase from each Amidah "gomeil chassadim tovim," it is important to understand each word individually. So what is the meaning of "chassadim?"
We are actually more familiar with a different form of this word, "Chassid," usually transliterated as "Hassid." The Hassidim are the devotees of a particular approach to Judaism initiated by the great Rabbi Israel Baal Shem Tov. Today, the surviving sects follow the teachings of various descendants of his disciples. The word itself means "pious ones" and has applied to different groups of especially devoted Jews in early rabbinic times and medieval Germany.
Another word from the same root is "chassidah," Hebrew for "stork." The stork is the fabled messenger of birth in American culture, evoking compassion, but too few of us have seen one in flight. On the ground, it looks unlikely to get airborne, but once aloft the stork is graceful and beautiful.
And we are also more familiar with the singular form of chassadim, "chessed," which we encounter often as part of the triumvirate "Chen, Chessed and Rachamim" (which sounds like a Jerusalem law firm). Chessed usually translates as beneficence or loving-kindness, but I prefer simply the word "love." This love is different than "ahavah," which is an investment in a relationship. Chessed, chassadim, are selfless acts of love that are performed purely out of devotion to the object of one's affections. They are performed primarily without expectation of reciprocation.
That's what piety is – devotion to selfless acts of love for God's benefit. There is an unlikely aspect to such devotion; it is hard to believe such actions can actually take flight, but their grace and beauty are unmistakable.
To speak of God's "chassadim" toward us is to speak of selfless acts of devotion performed to our benefit. They are unlikely except as experience has taught us to appreciate the piety of God's nature. And they have elements of both grace (chen) and compassion (rachamim) that bridges the regal and earthy elements of the Divine One.
How "chassadim" relates to the word preceding and the one following in this phrase is the subject of another discussion.