Graded potentials are changes in the membrane potential of a neuron or muscle cell that vary in size, as opposed to being all-or-nothing like action potentials. These changes occur when ions flow across the cell membrane, leading to local changes in voltage that can either depolarize or hyperpolarize the cell. The magnitude of a graded potential is proportional to the strength of the stimulus, and they play a crucial role in initiating action potentials and overall cellular communication.