Based on the description provided, the type of modern art in which the work itself is made of an action performed by an artist, sometimes for an audience, is called Performance art.
Performance art is a form of contemporary art where the artist uses their body, presence, and actions as the medium of expression. It often involves live performances that can include elements of theater, music, dance, and visual arts. The artist's body and the actions performed become the artwork itself, blurring the lines between art and life.
One famous example of performance art is "The Artist is Present" by Marina Abramović, where she sat silently across from museum visitors for hours at a time. This piece exemplifies how performance art can challenge viewers to rethink the boundaries of art and the role of the audience in experiencing it.