Understanding regularization
That's correct. Without regularization your model would fit to an irrelevant noise present in your dataset. It means that training set will fit better but the overall predictive power will decrease. This is a good article about overfitting and regularization.

Also you can get some intuition by watching these images:
Without regularization
With regularization
You can clearly see that the shape at the 1st image has problems with prediction at the upper left corner but it perfectly fits to the training points.