This article concerns secularity, that is, being secular, in various senses.
The word "secular" comes from a Latin word meaning "happening once in an age". This offers the opportunity for a confusing variety of meanings. A dog is "big" compared to an ant but not compared to an elephant, and "secular" is similarly subject to "relative to what?" ambiguity. But secular also means, in different contexts, long (relative to something else) because an "age" is a long time, and (relatively) short because an age is "not very long compared to eternity".
Secularity as relatively long duration
In astronomy, "secular" is used in ways that draw on the "long time" emphasis, and implies contrasting phenomena whose periodic repetition astronomy observes, with secular ones that either repeat too slowly to observe (or are understood not to go through cycles, no matter how long). In particular, astronomical ephemerides use "secular" to label long-term perturbations in the motion of planets, as opposed to periodic perturbations. (See month.)
Secularity as relative worldliness
The Christian doctrine that God exists outside of time led medieval Western culture to fix the meaning of "secular", in contexts related to religion, as indicating the direction away from religious affairs and toward "worldly" (or "temporal", time-related) ones, and this has been extended to apply relative to all religious or spritual beliefs, whether or not they include a similar doctrine.
One example is "clerical authority" (referring to matters the church controls) as opposed to "secular authority" (referring to feudal power).
Nevertheless, "secular clergy", for instance, is no contradiction, but rather describes a parish priest, who is secular in comparison to a "religious", a noun referring to a person subject to monastic vows.
A separate article discusses the various senses of "secularism" in the personal, social, and political spheres, based on this same contrast between religious or spiritual matters on one hand, and secular or worldly matters on the other.
The next section contrasts secular in the sense of long term versus short term:
In numerical descriptions, such as of a time series of numbers, a secular trend is the long-term trend in the numbers (up or down), as opposed to a smaller cyclical variation in the time series, with a periodic short-term duration.
For example, in the business operating cycle, revenue might fluctuate during the fiscal year; an experienced management can then ignore the cyclical fluctuation in revenue, and concentrate on the 'year over year' trend, hopefully a secular trend upward.
Secular in its most common meaning, means "outside of religion". It can be used in a neutral sense, e.g. when at the end of the 17th century most sonatas were used in church services, a "secular" sonata meant nothing more than a sonata not used in a church service (without any connotation of the composer being religious or not). See secularity as relative worldliness.
In current political and philosophical discourse, it refers to a government obeying civil laws (as opposed to religious instructions like the Islamic shariah, the Catholic canon law or rabbinacal law), independently from any religion, and not favoring any particular religion; in addition, secularism also includes the priority of the civil laws over any religious legislation. Nowadays, all major religions accept this, except for significant schools in Islam (which proclaim just the opposite).
On the other hand, secular can have the connotation of a dismissive conviction regarding religious matters: see secularism.