Some science behind the scenes
A neurotransmitter is a type of chemical. Within the Physical nervous system, a neuron affects other neurons by releasing a neurotransmitter that binds to chemical receptors. At the synapses, a store of these chemical messengers – neurotransmitters – is kept ready for release. You can see this in the diagram below from Wikipedia. The axon terminal of one cell connects up with another neuron's dendrite, via a synapse.
When a signal reaches the axon terminal, it opens voltage-gated calcium channels, which causes the synaptic vesicles filled with neurotransmitter molecules to fuse with the membrane, releasing their contents into the synaptic cleft. The neurotransmitters diffuse across the synaptic cleft and activate receptors in the next neuron.
The effect upon the target neuron is determined not by the source neuron or by the neurotransmitter, but by the type of receptor that is activated. A neurotransmitter can be thought of as a key, and a receptor as a lock: the same type of key can here be used to open many different types of locks.