Hi Drhuv! Thanks for stopping by!
A pendulum isn't really a "term," it's an object. A pendulum is basically a weighted object hanging from some kind of base. If the base is moved, that weighted object is going to swing side to side. Many clocks are pendulum clocks (such as "grandfather clocks") which you'd recognize by the swinging pendulum beneath the clock face.
We use pendulums in our animation exercises because the idea of a pendulum clearly illustrates the concept of "successive breaking of joints" and overlapping animation.
Let's simplify the idea of a pendulum and imagine a base and a weighted object hanging from the base, with two joints connecting the weighted object to the base. Well, let's say someone kicks the base. What's the going to happen to the weighted object? Well, nothing at all, at first! First the base must move, which will move the first joint hanging down. Then the next joint will get moved. THEN the weighted object will get moved. The energy needs to travel down that chain of events to finally reach its destination at the heavy object, right?
This idea is something that we use throughout the body when animating. The spine is, in a way, in inverted pendulum rising up from a "base" (the hips). The arms can be thought of as pendulums hanging from the shoulder in certain circumstances. The tail of a critter is kind of a pendulum hanging from their backsides. The way a tree sways in the wind might be like an inverted pendulum connected to the ground.
The pendulum movement teaches us about a wave action that happens in any multi-jointed or organic object, and that's why you probably see it mentioned around animation sites.
Hope that answers your question! Thanks for writing in, Drhuv!