A nerve cell is a cell all by itself. There are two kinds of nerve cells, neurons and neuroglia. A single nerve cell can be part of a group of similar nerve cells and be considered a tissue; as in a nerve, which is composed of many nerve cells.
But, if there is more than one kind of tissue that contributes to a common function, then we call that an organ. The the heart is an organ because it has several kinds of tissues that all work together. Nerves contain a network of nerve cells that carry signals and impulses to the spinal cord and the brain. These are called afferent neurons. They also carry signals away from the central nervous system (CNS), these are called efferent neurons.