The nervous system of a grasshopper, like that of a human, can be divided into peripheral and central components. The peripheral nervous system consists of the sensory system, which tells the animal what's going on in its environment (internal as well as external), and the motor system, which carries the commands which control the muscles. The central nervous system, which in humans consists of the brain and spinal cord, in insects consists of the ventral nerve cord.
The ventral nerve cord, as its name suggests, is a cord of nervous tissue that runs the length of the animal in the lower part of its body. Grasshoppers are segmented animals, and each segment is controlled by its own ganglion. A ganglion is a package of neurons, containing anything from a few dozen to hundreds of thousands of neurons. The ganglia of each segment are joined to their neighbours by the interganglionic connectives (although some ganglia are fused directly together). Thus the ventral nerve cord consists of this chain of linked ganglia.
The ganglia do the "thinking" of the nervous system, while the job of the interganglionic connectives is to coordinate the segments, so that the various bits of the animal all act together. Some ganglia, such as the brain, contain a particularly large number of neurons. In insects this is mainly because the brain has to deal with the sensory information coming in from the eyes and antennae, rather than because it does a lot of deep thinking. In fact, although the brain has some overall control over the animal, the rest of the central nervous system can do quite well without the brain being present at all. It is a rather gruesome fact that you can cut the head off an insect, and the rest of the body can walk, fly, mate and generally carry on apparently as normal (at least for a while...).
One of the advantages of studying the nervous systems of invertebrates is that they have far fewer neurons than vertebrates. Not only that, but in invertebrates such as grasshoppers, individual neurons can often be recognised from animal to animal. This means that one can study the properties of single identified neurons, confident in the knowledge that you can visit the same homologous neuron time and again, in different individual animals. This is in contrast to the more complex vertebrate animals, where any particular neuron can usually only be identified in terms of belonging to a particular class of neuron, rather than as an individual neuron in its own right.
One area where the simplicity of organisation of invertebrates is quite striking is in the motor system, i.e. the set of neurons which control mucle contraction. In a typical vertebrate, a muscle such as the biceps muscle of the forearm may have hundreds, or even thousands, of motorneurons controlling it. In the grasshopper, which is typical of many invertebrates, the extensor tibiae muscle has only 4 neurons controlling it, and only one of those is important in jumping.
One feature which compensates for the small number of motorneurons in insects is that the neurons are highly specialised compared to the motorneurons found in vertebrates. Thus each of the 4 neurons going to the extensor muscle in the grasshopper has different properties and does a different job:
The picture below shows an example of a metathoracic ganglion (the one controlling the hind legs) in which the FETi on one side has been stained with the fluourescent dye Lucifer Yellow. The bright blob on the right is the cell body of the neuron, which contains the nucleus. The fairly thick thread-like structure coming off the cell body is the neurite. Fine branches called dendrites arise from the neurite, and spread towards the middle of the ganglion. These are the structures that make and receive synaptic connexions with other neurons. The neurite eventually becomes the axon, which leaves the ganglion and carries nerve impulses to the muscle.
