It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but excluding the output neurons) has a probability \( p \) of being temporarily dropped out, meaning it will be entirely ignored during this training step, but it may be active during the next step.
The hyperparameter \( p \) is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore. It is viewed as one of the most popular regularization techniques.