Ordinary Time refers to all of those parts of the Catholic Church's liturgical year that aren't included in the major seasons (Advent, Christmas, Lent, and Easter). Ordinary Time is a feature of the current (post-Vatican II) liturgical calendar. In the traditional Catholic calendar (before 1970), the Sundays of Ordinary Time were referred to as the Sundays After Epiphany and the Sundays After Pentecost.
Ordinary Time begins on the Monday after the first Sunday after January 6 (the Feast of the Epiphany). In most years, that Sunday is the Feast of the Baptism of the Lord (see When Is the Baptism of the Lord?). In countries such as the United States, however, where the celebration of Epiphany is transferred to Sunday (see When Is Epiphany?), if that Sunday is January 7 or 8, Epiphany is celebrated instead. As feasts of our Lord, both the Baptism of the Lord and Epiphany would displace a Sunday in Ordinary Time. Thus the first Sunday in the period of Ordinary Time is the Sunday that falls after the first week of Ordinary Time, which makes it the Second Sunday of Ordinary Time.
Ordinary Time is called "ordinary" simply because the weeks are numbered. The Latin word ordinalis, which refers to numbers in a series, stems from the Latin word ordo, from which we get the English word order. Thus, Ordinary Time is in fact the ordered life of the Church. It's appropriate, therefore, that the Gospel for the Second Sunday of Ordinary Time (which is actually the first Sunday celebrated in Ordinary Time) always features either John the Baptist's acknowledgment of Christ as the Lamb of God or Christ's first miracle—the transformation of water into wine at the wedding at Cana.
Thus for Catholics, Ordinary Time is the part of the year in which Christ, the Lamb of God, walks among us and transforms our lives.