Overfitted models tend to have largely different (some very high, some comparatively low) coefficients/weights for different feature values. So, this means the model (when drawn as graph) will have high variation in slopes and even a small change in training data value (feature value) can lead to large change in output. To smoothen the overfitted model/curve that has high slope variation, we use regularization (example: L1/L2).
L1 regularization removes unnecessary/less influential features from the model making the model less complex. It does so by changing the weights/coefficients of such features to 0. So, this regularization is useful when we have many unnecessary features and is also considered useful for feature selection.
L2 regularization shrinks/adjusts extreme weights and results in a set of weights that are more evenly distributed. Unlike L1 Regularization, it does not result in weights of features being 0. So, this regularization is a little better when we know that all/a majority of the features are useful for the model.