All lifeforms need some method of moving substances around within themselves. Single-cell organisms use methods similar to those used by the cells of the multi-cellular, the natural spread of molecules from areas of high concentration, a process called diffusion, being a major one. Most plants carry their nutrients in water, from their root systems to their leaves, up tubes called xylem. They carry the food (sap) they manufacture in the main from sunlight and carbon dioxide, in another system of tubes called phloem, from the leaves to every other part of the plant, right down to the tiniest rootlet.
In the Animal Kingdom there are three types of circulatory systems used for this purpose. They are called cardiovascular (CV) systems as all have a heart and one or more blood vessels. The more complex the animal, the more complex the system. The simplest consist of a single open circuit; all invertebrates, animals without a spine such as worms and insects, have a single open circuit. More complex and more efficient is the CV system with a single closed circuit; this is the type that all fish species have. The most complex and efficient CV system has two closed circuits. This is the type all vertebrates beside fish have. Vertebrates are animals with a spinal column made of vertebrae, including all reptiles, birds and mammals. People are mammals.
So the first and perhaps most significant difference between open and closed circulation systems is that invertebrates have open circuits while vertebrates have closed. The second might be the size of animal they can support.
Elephants, giraffes and blue whales are all very large animals capable of living long lives with two closed circuits. Invertebrates such as beetles, flies, spiders and worms are much smaller animals with far shorter lifespans. They are limited in size in part because they do not have specialized organs for gas exchange, like gills or lungs, and in part because their open circulatory systems are less efficient at supplying the needs of their bodies.
A closed circuit is basically a series of connected tubes called blood vessels that make a circuit first leading away from the heart and then back to it. It starts with arteries that flow into capillaries that flow into veins that flow back into the heart. The largest artery is called the aorta.
An open circuit has a single blood vessel called an aorta that goes from the heart in the abdomen of an invertebrate to the head. The circulatory fluid flows out into the head cavity and slowly back through the animal's body cavities to the rear of the abdomen where it is pulled into the heart by its pumping actions. An invertebrate's heart is a series of chambers with attached muscles that contract and relax to suck in the circulatory fluid and pump it forward. So an open circuit has an artery, but no capillaries or veins.
The last difference is the circulatory fluid that is moving around these CV systems. Vertebrates have blood which is red because of the iron at the center of the hemoglobin proteins in the erythrocytes (red blood cells). These are necessary because the most important substance our circulatory system circulates is oxygen, most of which is carried by the hemoglobin.
Invertebrates circulate a fluid called hemolymph, which is generally a green color. While the purpose of both types of circuits is to move substances from one part of the body to another, hemolymph does not carry oxygen so needs no hemoglobin. Invertebrates "breathe" through their outer surfaces using an independent system of tubes, called spiracles, with only limited control over air-flow.
Closed circuits evolved from open circuits because they are more efficient and effective. In combination with a respiratory system with a specialized, muscle-powered gas exchange organ, they allow the development of much larger multi-cellular animals. Having the respiratory organ (lungs) on a second closed circuit, increases the efficiency to the point where animals are able to evolve quite large brains, if needed.