The concept of initiation is important in many Pagan traditions, where it marks a persons progress through various stages, from newcomer to experienced practitioner.
For instance, when a person joins a Wiccan coven, s/he learns the basics of ritual and the underlying ideas (the oneness of life, deity as Goddess as well as God and spiritual autonomy). If the person and the group mutually agree, s/he is initiated. This usually requires being with the group for at least a year and a day.
The initiation ritual marks the persons formal admission to the group, and by extension to the groups tradition (denomination). At this point a person is considered a priest or priestess, that is, knowledgeable enough in the Wiccan path to be responsible for his or her own spiritual progress and able to perform his or her own rituals.
After at least another year and a day, a person is eligible for another initiation to become a second-degree witch. This makes him or her a high priest or high priestess, who can perform rituals for and with the group, and help newcomers learn the craft. After yet another period of time, a person may have a third initiation and become an elder, at which time s/he may hive off and start another group (or stay and help the original group).
Various groups differ in the time required before each initiation and the amount of training or work involved. Some groups also offer a preliminary dedication ritual by which a person celebrates setting out on the Wiccan path.
Many groups dont follow the traditional pattern. Some reject any hierarchical structure and only do a single initiation since they dont elevate anyone everyones equal. Some casual groups dont do initiations at all. Many solitaries do self-initiation, simply declaring themselves to be full-fledged witches. Since Wicca has no central authority and no universally agreed-on procedures, these people are as legitimate as anybody else.
Initiation ceremonies have a reputation for being scary, the idea being to imitate ancient rites of death (of the person as s/he was) and rebirth (into a new spiritual state). However, there is no great mystery these days as to what goes on in secret initiations, the details of which can be found in many books such as The Witches Way, by Janet and Stewart Farrar (Phoenix Publishing, 1986).