Short answer
Brain cells communicate with each other with both electrical and chemical signals. Because of the structure of the cells, electrical signals can travel from one end to another within a cell. At the end of the cell, this electrical signal stimulates the release of substances called neurotransmitters that travel between cells to the next cell, to once more initiate an electrical signal. This is how signals are communicated between cells.
Longer answer
The brain has a lot of responsibilities, accumulating into a complicated task list. In order to work and achieve all tasks, the many parts of the brain need to collaborate and receive, evaluate and send information: this means that a good communication system is essential! The brain is equipped with cells called neurons, which are specifically designed for this important type of communication. In order to understand how one neuron communicates with other neurons, we first have to take a look at their basic structure.
A neuron is made up of three main parts; a cell body, dendrites, and an axon. The cell body contains the nucleus, the “control system” of the cell that contains all the important information. This cell body connects to the dendrites. Dendrites are branching extensions that resemble tree branches. With these branches, the neuron can receive information from other neurons, or from the outside world (via our senses). On the other side of the cell body is the axon: a single extension of the cell body. The axon is the side through which the neuron sends information. At the end of an axon are little knobs, called the axon terminals, through which information flows to other neurons.
The near-meeting point of the dendrite (the receiving part of the neuron) and the axon-terminal (the sending part of the neuron) is called a synapse. While the synapse is a very small gap that does not physically connect these parts of the two neurons, it is an essential part that needs to be bridged for communication between neurons to take place. In the following paragraphs, we will explain why:
When neurons communicate with one another, two different kinds of communication take place; within a neuron and between neurons. Within a neuron, messages are electric! The electrical signal starts in a dendrite and travels very fast down the neuron all the way to the axon terminal. This is called an action potential. When the action potential has reached the synapse at the axon terminal, the electrical signal is turned into a chemical signal. This is because a chemical signal will be able to bridge the gap of the synapse, while the electrical signal can’t. Furthermore, a chemical signal can transfer more information than an electrical signal, since there are different chemical components.
The chemical signal works as follows; the electrical signal at the end of its journey through the neuron causes the axon terminal to release little chemicals, called neurotransmitters. Neurotransmitters, such as dopamine and serotonin, each have a specific purpose; they can either excite or inhibit a neuron. When released, they travel across the gap of the synapse all the way to the dendrite of the next neuron. There, neurotransmitters attach to the neuron and cause a response. When this response is strong enough, it is turned into an electrical signal, called an action potential, which restarts the cycle. When this happens, the electrical signal travels down the neuron to the next synapse, in order to bring the message to another neuron. In this way, neurons communicate all the way through our bodies.
References
Gazzaniga, M. S., Ivry, R. B., & Mangun, G. R. (2014). Cognitive Neuroscience, the biology of the mind. W. W. Norton & Company.