Neuropil is the brain tissue that lies between the cell bodies.
Traditionally, when pathologists looked at brain tissue they concentrated on neurons (the active functioning cells of the brain), glial cells and axons (especially in white matter, which is mostly composed of axons and glia cells). Neurons are the cells that perform the actual processing of information. Glia cells have 'supporting' functions in a very loose sense of the word. Also, most brain tumors arise from glial cells.
On a coarse scale nervous tissue (ignoring blood vessels etc.) is composed of the cell body of the neurons and glia cells and their processes or protrusions. For neurons, these are dendrites, dendritic spines and axons. Dendrites collect input from other neurons, which is processed by the neuron (in dendrite and cell body) and propagated to other cells via axons, which you may view as special cables. At the end of an axon synapses are formed, serving as a chemical junction to other cells. The neuropil is what is left when you take away the cell bodies of neurons and glia from the tissue, i.e. the tangle of dendrites, axons and glial processes.
further reference on Neuropil: Roche Enzyclopedia of Medicien, Dictionary Barn