The western church sees the day as commemorating the visit of the Magi (the "wise men") to the baby Jesus at the manger; the eastern church sees it as the day commemorating the baptism of Jesus in the River Jordan at the hands of John the Baptist. The arguments are ancient, though the steam for each viewpoint has long dissipated.
The significance of the day is the same for both traditions. Epiphany marks the end of the 12 days of Christmas, and is a reminder of the true significance of Christmas: that God chose to walk among us as a human being, to show us that being human (and having a human body) is good; to light our way to live and love without fear of death. All of those lessons will unfold for us as the year progresses; how we hear those lessons (and if we hear them) remains our challenge.
For now, may you bask in the winter light of Epiphany; may you find wisdom and strength for all you do, and may many blessings fill your path.
Painting, "Epiphany Times Three," by Kathrin Burleson.