When you train your neural network on a given dataset, then it learns the underlying patterns that describe the relationship among the data points of the given dataset. Some of these are general patterns, while other are inherent to the data points of the training dataset.
General patterns are those patterns which would still be present when new data is fed to the network. While patterns inherent to data points of the training dataset are classified as noise.
Presence of noise leads to model overfitting. Further, our primary & sole aim is to learn the general patterns, hence learning/presence of noise leads to waste of time and computational resources.
This is where regularization comes in. It restrains the learning process to general patterns and prevents noise from being taken into account i.e. it regulates the learning process. Thus checking model overfitting.