"Mystery" seems to be an indispensable category, especially for the language of Catholic Christianity. My own concept of mystery, which follows, is rooted in the nature of persons...
A mystery is some hidden truth that is difficult (but not impossible) to attain. A mystery is hidden within the interior privacy of a person. A person reveals his- or herself only voluntarily---no force can extract it! Furthermore, the recipient must be attentive to the revelation.
This personal truth is hidden in another sense because a mystery revealed remains a mystery. We never come into full intellectual possession of a person, no matter how many times he or she self-reveals. The same is true of mystery. The encounter with mystery is itself mysterious.
And this personal truth is hidden in yet another sense because a mystery is very difficult to mediate to a third person. We can point to it with words, pictures, and dramatization, but these things are very easy to ignore or distort on the receiving end. The mediation of a mystery to a third person is also mysterious.