Final answer:
The fine extension that transmits impulses away from the neuron's cell body is the axon, which is essential for nerve signal transmission and communication with other cells.
Step-by-step explanation:
The fine extension that conducts impulses away from the cell body of a neuron is the axon. Each neuron typically has a single axon, which serves as a conduit for electrical signals known as action potentials. These action potentials travel from the neuron's cell body down the axon to reach the axon terminals. At these terminals, the electrical signal is converted into a chemical signal, which then crosses the synapse to communicate with other neurons, muscle cells, or glands. The axon is crucial in the transmission of nerve signals and ensuring rapid and effective communication throughout the nervous system.