What does calling fit() multiple times on the same model do?

Question

After I instantiate a scikit model (e.g. LinearRegression), if I call its fit() method multiple times (with different X and y

Answer 1

You can use term fit() and train() word interchangeably in machine learning. Based on classification model you have instantiated, may be a clf = GBNaiveBayes() or clf = SVC(), your model uses specified machine learning technique.
And as soon as you call clf.fit(features_train, label_train) your model starts training using the features and labels that you have passed.

you can use clf.predict(features_test) to predict.
If you will again call clf.fit(features_train2, label_train2) it will start training again using passed data and will remove the previous results. Your model will reset the following inside model:

• Weights
• Fitted Coefficients
• Bias
• And other training related stuff...

You can use partial_fit() method as well if you want your previous calculated stuff to stay and additionally train using next data

Answer 2

If you will execute model.fit(X_train, y_train) for a second time - it'll overwrite all previously fitted coefficients, weights, intercept (bias), etc.

If you want to fit just a portion of your data set and then to improve your model by fitting a new data, then you can use estimators, supporting "Incremental learning" (those, that implement partial_fit() method)