Patricia Sanchez from the National Catholic Reporter connects the Eucharist and being at one with God with the events that led up to the Crucifixion.
Basically, Sanchez's logic goes something like this. We (Catholics) are in union with God by means of Holy Communion. This union is special, because it helps us become better people, and because it leads us to do the "right thing", even though the right thing may seem illogical and may cost our lives. The events that led up to the Crucifixion (the verses that lead up to John 19:26-27) show that Jesus's willingness to take the punishment for our sins is illogical, hence noble and admirable in an empathetic sort of way.1
A Catholic reference2 offers two likely interpretations of the verse. One is the literal interpretation: that Jesus is concerned for his mother. The other is the symbolic interpretation: that Mary, mother of Jesus, may be perceived to be the mother of all Christians, personified by the Beloved Disciple. Mary may be a representative to those seeking salvation, and she is supported by the disciple who interprets Jesus' revelation, or perhaps, the verses are about Jewish and Gentile Christianity being reconciled.2
I make a note that the National Catholic Reporter has received significant controversy from the Roman Catholic Church, because it promotes beliefs contrary to what the Vatican teaches. It merely gets its name, because it intends to write for progressive-minded Catholics or cafeteria Catholics.
Sánchez, Patricia Datchuck. "And I In Them." National Catholic Reporter 46.14 (2010): 27. Academic Search Premier. Web. 17 Jan. 2015.