Regularization is the collective name for techniques that make it harder for a model to memorise its training data, which brings overfitting down. The idea is plain: teach the model that being needlessly complex has a cost, not just being wrong. That cost arrives as a penalty term added to the loss function.
The two most common forms are L1 and L2. L2 penalises the squares of the weights and pulls them toward zero, so no single feature can take on outsized weight. L1 penalises absolute values and drives some weights exactly to zero, which amounts to implicit feature selection. In neural networks dropout does the same job by switching off random neurons during training so the model cannot depend on one path. Early stopping and data augmentation belong to the same family.
Strength is a balancing act. Too weak and the model memorises anyway, too strong and it cannot learn the data at all, which is underfitting. The right value is picked by watching the validation score.
A concrete case: a bank predicts credit risk from 80 variables. Without regularization the training score is very high and live behaviour is erratic. Adding an L1 penalty drives 23 of the 80 weights to zero, and the model becomes both simpler and steadier in production.
Regularization does not paper over missing data. If there genuinely are not enough examples, a penalty term only hides the problem.