Adept is a person trying to advance enough on the path of spirituality to become a master.
In Magic, an adept should possess considerable magical knowledge (rituals, spells, divination, psychic powers). They should be initiated in the art of alchemy and possess power over the four elements.
In spirituality, an adept should strive to achieve enlightened consciousness.
A term closely related to the Adeptship is “the great work“. It takes a lot of time, if not multiple incarnations, to complete the process and become an Adept. Therefore this expression.
The secret knowledge is revealed to the Adept over time. Step by step, the Initiate will complete this great work in due time. They will then attain a perfect union between the body, soul, and spirit.
The origin of the word “adept” seems to be derived from Latin expression, adeptus, meaning “the one who has attained” (the secret of transmuting metals).
Dr Claude Brodeur, PhD, say about the path of the Adept :
This path is not for everyone. It is for those who have come to realize that an inner world exists. This world is as real as the world we see, hear, feel, and touch. This inner world far surpasses in importance the external world of manifestation.
Gnosis.org writes on the Hierarchy of Adepts , or the Great White Brotherhood of Spiritual Masters. In this sense, an Adept should be understood as a highly developed spiritual person.
Here is what the Sanctus Germanus website  says about the Adept of the Brotherhood:
To become a perfect adept takes long years, but at last he becomes the master. The hidden things become patent, and mystery and miracle flee from his sight forever. He knows how to guide force in this direction or that — to produce desirable effects. The secret chemical, electric or vital properties of plants, herbs, roots, minerals, animal tissue, are as familiar to him as the feathers of your birds are to you.
The Theosophical doctrine defines the process of Adeptship  as follows:
Adeptship is the identity of the innermost self of man with the innermost self of the universe, the Atma with the Paramatma, pseudo-individuality is dissolved. The Adept abides in perpetual experience of identity with Universal Spirit. This is Perfection, Nirvana or Salvation – liberation from illusion of separated individuality. This is the highest human attainment and the spiritual “purpose” of existence.
Photo by Moyan Brenn