Rabbi Arieh Kaplan's book on Jewish Meditation provides a good overview on the history of Kabbalah, explaining along the way why it's called 'Kabbalah'. So for people using 'Kabbalah' in the classic sense of a received tradition, i.e. what it literally means, here's the explanation for that, per R' Kaplan:
Kabbalah is the study of the Torah on its deepest, metaphysical level. In Hebrew it's also known as 'Sod' or 'secret' or 'Pnimiut' i.e. the innermost Torah. Studying and applying Torah on this level can lead one to extremely high spiritual levels that Rabbi Kaplan explains could be more desirable than any physical pleasure. When achieved through Torah, it required a lot of self-discipline and extraordinarily good behaviour - i.e. it was hard work. And yet there were schools for this with large numbers of students, suggesting that the draw of being close to G' and experiencing the supernatural was very desirable.
However it could also be achieved through specific impure means, associated with idolatry.
When Bnei Israel were in their land, our leadership could do a fair amount to prevent and avoid the risks associated with idolatry. Once exiled and dispersed, the temptation to achieve exalted spiritual states through impure means was greater and harder to fight. It would have been easy for Bnei Israel to break up into a lot of different cults, bestranged from the Torah, in such a concept.
Therefore to protect the Jewish people's unity and avoid them sinning with idolatry and various related impurities, significant parts of Kabbalah were hidden away and no longer taught to the masses. The idea being to dial back the desire for such extreme spiritual experiences as are available through Kabbalah, and thus prevent people seeking them also through impure means that would require less work and be more accessible in a non-Jewish environment.
As such, the deepest aspects of Kabbalah are taught only one-on-one as @Avi indicated and I believe a variety of sources (e.g. Rambam) indicate, and even so only to extremely capable students, and even so only in abbreviated/hinting form, leaving it to the student to grasp most of the material on their own. Hence it is a received tradition, passed on from teacher to student for generations.
p.s. As I understand it, there are different levels within Kabbalah. Just as there is Pshat (basic), Remez (allusions/hints), Drash (expounding) and Sod (secret) at a general level, so too there is a subdivision within them along the same lines. So there is Pshat within Sod, and the deepest level of Kabbalah would be Sod within Sod.
Amongst native Israelis, I believe that Kabbalah is generally understood to refer to this, and especially to its practical application by such masters as the Baba Sali or R' Itzhak Kaduri.