"Does not seek its own" is the next quality of love. If we understand Jesus' work on the cross, this is probably the easiest to understand. It is a statement of love's willingness to sacrifice.
Love is always looking outside of itself. Love looks to serve, to give. It is generous. During new testament times, there was a region with a famine. Food was scare and expensive. A poor church collected money that they could not afford to give, but did, sending the money to help churches in the famine stricken region. In our economically difficult times, image churches in Africa sending money to help churches in the US, Canada and Europe. People living on $400 a year, sending some of that to people in more affluent countries to ease their burdens.
It is that willingness to sacrifice, and choosing to sacrifice, to help others is the essence of love. And in an age of "me first," that aspect of love stands out like a beacon in the dark.