Each neuron is a small information processor with a cell body, multiple inputs called dendrites, and output extensions called axons. They communicate with each other via synapses, small gaps where signals pass from one neuron to the next.
To put it simply, you can think of neurons as the wiring in a super-complex computer (your brain). They transmit information throughout the system, allowing different parts of the brain to communicate with each other and the rest of the body, enabling everything from moving your fingers to forming a memory.