Applying an action to a point results in a transformed point. Similarly, applying an action to a group of points results in a transformed group. In the example below, the group of points are part of the same space, the 2-D real space. The applicable actions can be thought of as acting on the entire space.
The concept is a simple one, but is an important starting point to understanding how one member of an antomical "family" (orbit) can be transformed into another member of that "family". Two different actions have been applied to the space of the stomach below, resulting in two significantly different looking stomachs. The top group action is a 20 degree horizontal shear. The bottom group action is a 20 degree vertical shear.