Egalitarianism is the general idea of equality. The egalitarian idea is that people, no matter what their race, gender, religion, etc., are all equal in value. Egalitarianism in politics means that both male and female are equally capable of holding an office.
Within Christianity, however, egalitarianism is the position that both male and female are equal in ecclesiastical authority. In other words, according to the egalitarian view it is permissible for women to hold the offices of pastor and elder where leadership is exercised.
Though the Bible teaches the equality between men and women (Gal. 3:28), it supports the differentiation of roles between them. Most importantly, this is manifested in the context of church leadership where women are not to teach or exercise authority over men (1 Tim. 2:12) based upon the created order (1 Tim. 2:13). Likewise, elders are to be male (1 Tim. 3:2; Titus 1:6).