In simple terms, neurons are cells that connects 2 other cells, carrying information between them; a bit like a cable. The information is coded into electrical signals, known as action potentials, or impulses. Neurons receive information in the form of chemical signals (neurotransmitters) released from neighbouring cells at a junction called the synapse. Electrical signals are generated at the postsynaptic terminal of a neuron and conveyed along the dendrites and axons of a neuron to the presynaptic terminal. At the presynaptic terminal, the electrical signals trigger the release of neurotransmitters into the synaptic junction with another neuron/cell.
In Reality: Neurons are rarely as simple as the information carrier described above, the neuron pictured on the left (bright green due to a fluorescent marker), has multiple dendrites, each leading to multiple synapses the neuron receives information from. These complex neurons can act as processors, converting inputs from multiple sources into sequences of action potentials within the axon that create a meaningful output at the next synapse.