In John 19:26-27, we read, “When Jesus saw his mother and the disciple whom he loved standing nearby, he said to his mother, ‘Woman, behold, your son!’ Then he said to the disciple, ‘Behold, your mother!’ And from that 
hour the disciple took her to his own home.” Since John is referred to as the disciple that Jesus loved, it’s been the tradition that he was the disciple that Jesus addressed from the cross. Early Church History bears this out as well. Mary is not mentioned by name, but it’s clear who he was referring to.
It’s a remarkable thing. Here Jesus is, suspended above the earth by nails driven into his hands and feet with a crown of thorns on his head, dying the most painful death imaginable and he’s focused on the needs of others. One write described the scene this way: “Here he is humiliated by being made a public spectacle. Sweat pouring off his body in the intense heat of the day. Flies swarming around his head. Blood dripping down from his head. And increasingly finding it harder and harder to speak. His posture on the cross put pressure on his lungs so that breathing was more and more difficult. And yet he turns his gaze toward his mother and speaks to her and then to the disciple who would become her son.”
Some argue that these words, in the simplest sense, might be like our concern for who would look after a loved one we’re gone. We might be concerned about who will care for our aged parents if we weren’t around to do so, but Jewish tradition required the children to care for their children and Mary had four other sons as well as at least one daughter. It wasn’t her physical needs that Jesus was concerned about. In my opinion, at the foot of the cross, men and women, all become part of a new family. Older women become like mothers. Younger women become like sisters and in the early church that’s what they were called. Men become my brothers, and lo and behold, a new family is established. Based not on the DNA contained in the blood of the physical parent, but according to the DNA of Jesus’ blood, there’s a new relationship between people who gather at the foot of Jesus’ Cross in faith. I’m sure there was loving concern for His earthly mother, but I can’t escape the fact that Jesus was expressing more than that. He was commending us to each other to be cared for and watched out for in the new family called the Church.