The Catholic Church has always divided the year into seasons during which specific aspects of the mysteries of Christ's life were celebrated. Before the Second Vatican Council, the Church began its liturgical year with Advent, beginning on the fourth Sunday before Christmas and running through Christmas Eve. The season of Christmas was next, running through the Epiphany (January 6). The next major season was Lent, from Ash Wednesday (the seventh Wednesday before Easter) until the day before Easter; then the Easter season itself, running through Pentecost, the seventh Sunday after Easter. The two remaining stretches of the year (six weeks or so after Epiphany and twenty-seven or so after Pentecost) were referred to as the Sundays after Epiphany (or Pentecost): thus the Second Sunday after Epiphany or the Eighteenth Sunday after Pentecost.
In 1963, the Second Vatican Council ratified the Constitution on the Sacred Liturgy known as Sacrosanctam Conciliam, intended to reform the liturgy "in order that the Christian people may more certainly derive an abundance of graces from [it]" (Sacrosanctam Conciliam, paragraph 21) In particular, the Council decreed:
The liturgical year is to be revised so that the traditional customs and discipline of the sacred seasons shall be preserved or restored to suit the conditions of modern times; their specific character is to be retained, so that they duly nourish the piety of the faithful who celebrate the mysteries of Christian redemption, and above all the paschal mystery.
Consequently, in 1969, the Vatican issued the Universal Norms on the Liturgical Year and the Roman Calendar, which discussed in detail the changes to be made. One of these was the introduction of the season of Ordinary Time, which replaced what had been the Sundays after Epiphany and the Sundays after Pentecost. The document defines Ordinary Time in this way:
Ordinary Time begins on the Monday which follows the Sunday occurring after 6 January and extends up to and including the Tuesday before the beginning of Lent1; it begins again on the Monday after Pentecost Sunday and ends before First Vespers (Evening
Prayer I) of the First Sunday of Advent2.
1That is, until the seventh Tuesday before Easter.
2The first Sunday of Advent is the fourth Sunday before Christmas. The reference is to the first official prayer service of the previous evening.
As the document states,
There remain in the yearly cycle thirty-three or thirty-four weeks [depending on the year] in which no particular aspect of the mystery of Christ is celebrated, but rather the mystery of Christ itself is honoured in its fullness, especially on Sundays. This period is known as Ordinary Time.
I have found no official discussion of the etymology of the term "Ordinary". The formal Latin term is "tempus per annum", that is, "time throughout the year". One source on the Church year states, without citing sources, that
Many sources, online and in print, suggest that Ordinary Time is derived from the word ordinal, meaning "numbered," since the Sundays of Ordinary Time, as in other seasons, are ordered numerically. However, other sources suggest the etymology of "Ordinary Time" is related to our word "ordinary" (which itself has a connotation of time and order, derived from the Latin word ordo).
Translations into other languages found on the Vatican's website seem to indicate the connotation may be "ordinary", "common", or "usual"—for example, the Italian translation of a homily by Pope John Paul II translates it (in the first paragraph of section 2) as "ordinario", and the Portuguese version translates it as "comum". Both those words appear to translate into English as "common", "ordinary", or "usual", indicating that John Paul II at least believed the phrase "ordinary time" meant "common or usual time".