The speaker of "Greedy" wants to be loved completely. Going through the list, they ask for the other person's thoughts, hands, eyes and soul, so nothing is held back. The title is an honest admission: the speaker knows this is a lot to want, and says so anyway.
What stands out is how the wanting moves from the outside in. It begins with touch and sight, then ends with the soul, which suggests the speaker cares most about real closeness rather than just attention. Twice they use the phrase "as if I am the only person", which shows a need to feel singled out and chosen above everyone else. That hints at some vulnerability underneath the boldness.
The mood is intense, hungry and a little breathless, but also tender. The last lines soften it, since the goal is to "fall in love with you more and more each day." The greed is really a wish for love that keeps growing.