Monkeyvoke's answer is a more strict pharmacological definition of an agonist/antagonist. In general:
Agonists increase the effect of a neurotransmitter on the synapse; this can be by directly activating the post-synaptic receptor or by indirectly increasing the effect of the neurotransmitter (i.e. increasing the production of the neurotransmitter).
Agonists inhibit the effect of the neurotransmitter on the synapse. This can also be direct (i.e. competitive inhibition of the post-synaptic receptor) or indirect (i.e. inhibitting release of the neurotransmitter).