Most of the animals that we are familiar with (think of any pets you've ever had) have bilateral symmetry: they have a head end and a tail end, a left and a right, and a top and a bottom. In scientific terms that translates to the anterior-posterior, left-right, and dorsal-ventral axes. Also, most bilateral animals are elongated on the anterior-posterior axis and have some sort of cephalization going on in the anterior end of the body; in other words they have a head, or at least a concentration of neural tissue and sensory structures in the part of the body that encounters the environment first.
Even your basic worm meets all these criteria. Here's a video clip of Nereis sp., an intertidal polychaete worm. The body is conspicuously segmented, as this animal is a somewhat distant relative of earthworms. The body symmetry is clearly bilateral, and you can see that it has an anterior end, which in this case is defined by both the direction of locomotion and the presence of a head:
As "normal" as bilateral symmetry may seem, there are many animals that have a completely different type of symmetry. The cnidarians, for example, are the largest group of animals with radial symmetry. This means that instead of being elongated along an anterior-posterior axis, these animals' bodies are either columnar or umbrella-shaped. In either case, when you look down on them you see a circular shape:
An animal with this sort of body plan obviously has no head--no eyes, nose, or concentration of either neural or sensory structures. Being a sea anemone, it lives attached to the sea floor and doesn't walk around much, so there's also no locomotory clue as to a possible anterior end, either. Rather than have most of its neural apparatus located in a particular region, its nervous system is diffusely scattered over the entire body. This animal has the advantage of meeting its environment from all sides and across all of its external surface. It can't be snuck up on, because it has no front or back.
Let's now return to the echinoderm pentaradial symmetry. As you might imagine, the five-way symmetry of echinoderms has strong implications both for other aspects of the animal's anatomy and the way that it interacts with its environment.
Take the example of a sea star:
Echinoderms are structurally more complex than cnidarians, with distinct internal organs. The central disc contains most of the organs, but there are extensions of both the gut and the gonads in each of the five arms. Although, like the cnidarians, the echinoderms don't have a centralized nervous system, they do have very simple eyes that can detect light and dark. And guess where, in an animal with a form of radial symmetry, the eyes are located? Hint: Think about how the animal encounters its environment. Yes, the eyes are in the tips of the arms, along with chemosensory receptors. Makes sense, doesn't it?
Pentaradial symmetry also affects how an animal locomotes. Since they have no front or back, sea stars and sea urchins can walk in any direction. They can also change the direction of locomotion easily, without needing to turn around the way we would.
There's a natural human tendency to regard creatures like us as somehow better than those different from us. I try to teach my students that complex is not always better (think of the pervasive damage done to a person who has suffered a major brain or spinal cord injury); that there are multiple types of complexity (morphological, behavioral, reproductive, and life cycle); and that the best way to understand an animal is to put yourself in its "shoes" and try to imagine what its life is like, with its anatomy, physiology, and lifestyle. It can be difficult to shed our human-centric biases, but we have to put them aside at least temporarily if we truly want to make sense of what's going on in the world around us.