The synapse is a method by which cells communicate with one another, it is a apposition of a process (usually an axon) of 1 neuron to the dendrites, cell body, or axon of a 2nd neuron. Axons send out impulses (messages) while dendrites receive them.
A synapse is how information is passed between neurons, for example; if you touch something hot, neurons will send messages to the brain (via synapses) which will inform the brain to move the hand.
A synapse occurs when the axon of one cell; and a dendrite of another come in "contact" (they do not actually touch; but rather "hover" over each other) with each other. Neurotransmitters are released from the pre-synaptic terminal (cell which is sending the "message"), and bind to receptors on the post-synaptic terminal (receiving the "message"). The cell will reset, so another synapse will be able to take place.
Each day hundreds of synapses are formed in our brain; its the greatest asset of our memory and learning as it is responsible for making connections between things; as well as association.