A catechumen is one who is preparing for baptism in the Church. In modern usage, catechumen can also refer to one who is preparing for chrismation (or another form of reception) to be received from a heterodox Christian communion.
In the ancient Church, the catechumenate, or time during which one is a catechumen, often lasted for as much as three years and included not only participation in the divine services but also catechesis, formal instruction from a teacher, often the bishop or appointed catechist. Exorcists often performed the catechetical role, as well, following their initial prayers of exorcism over the one being made a catechumen, which is the traditional manner of receiving a catechumen into the community of the Church.
Catechumens are understood to be Christians upon beginning their catechumenate, and should they die before baptism, they are traditionally given an Orthodox funeral.
As the Church eventually became the majority religion of the lands in which it sojourned, the catechumenate as an institution gradually died out in many places, as most Christians were being baptized shortly after birth. As Orthodoxy has moved into the West and Far East and begun gaining converts to the faith, the catechumenate has been significantly rejuvenated.
Catechetical instruction in Orthodoxy in America does not typically last the three years which was common in the time of St. John Chrysostom, but typically can last from six months to a year, depending on the practice of the bishop, his jurisdiction, and the level of spiritual maturity of the catechumen. Local parish priests typically oversee the catechesis of those preparing to be received into the Church.
The Orthodox Church has no formal catechism, a single body of work that details the specifics of its faith. This is one difference between the Orthodox Church and the Roman Catholic Church, who does have a specific catechism.