As a Carmelite Secular maybe I can help here. Secular means "in the world" as opposed to cloistered, "religious," etc. For instance, in my Discalced Carmelite Order, there are three memberships: the friars and nuns, both of which are "religious" and the lay, third order, or secular (all mean the same thing), which are not "religious" and do not live in community but live out the charism of the order "in the world." So in ecclesiastical language, secular means of or in the world.

Interesting aside: in the Gloria, "in saecula saeculorum" is said in the English western version as "world without end." I believe Byzantines translate it as "unto ages of ages."