What does the CV stand for in sklearn.linear_model.LogisticRegressionCV?

You are right in guessing that the latter allows the user to perform cross validation. The user can pass the number of folds as an argument cv of the function to perform k-fold cross-validation (default is 10 folds with StratifiedKFold).

I would recommend reading the documentation for the functions LogisticRegression and LogisticRegressionCV

Yes, it's cross-validation. Excerpt from the docs:

For the grid of Cs values (that are set by default to be ten values in a logarithmic scale between 1e-4 and 1e4), the best hyperparameter is selected by the cross-validator StratifiedKFold, but it can be changed using the cv parameter.

The point here is the following:

• yes: sklearn has general model-selection wrappers providing CV-functionality for all those classifiers/regressors
• but: when the classifier/regressor is known/fixed a-priori (to some extent) or sometimes even some CV-model, one can gain advantages using these facts with specialized code bound to one classifier/regressor resulting in improved performance!
  • Typically:
    • CV already embedded in optimization-algorithm
    • Efficient warm-starting (instead of full re-optimization after just the change of one parameter like alpha)

It seems, at least the latter idea is used in sklearn's LogisticRegressionCV, as seen in this excerpt:

In the case of newton-cg and lbfgs solvers, we warm start along the path i.e guess the initial coefficients of the present fit to be the coefficients got after convergence in the previous fit, so it is supposed to be faster for high-dimensional dense data.

May I also refer you to this section in scikit-learn documentation which I beleive explains it well:

Some models can fit data for a range of values of some parameter almost as efficiently as fitting the estimator for a single value of the parameter. This feature can be leveraged to perform a more efficient cross-validation used for model selection of this parameter.

The most common parameter amenable to this strategy is the parameter encoding the strength of the regularizer. In this case we say that we compute the regularization path of the estimator.

And logistic regression is one such model. That's why scikit-learn has the dedicated LogisticRegressionCV class that does this.

There are some things left out on other answers, e.g. about gridsearch functionality. See the docs:

cross-validation estimator An estimator that has built-in cross-validation capabilities to automatically select the best hyper-parameters (see the User Guide). Some example of cross-validation estimators are ElasticNetCV and LogisticRegressionCV. Cross-validation estimators are named EstimatorCV and tend to be roughly equivalent to GridSearchCV(Estimator(), ...). The advantage of using a cross-validation estimator over the canonical estimator class along with grid search is that they can take advantage of warm-starting by reusing precomputed results in the previous steps of the cross-validation process. This generally leads to speed improvements. An exception is the RidgeCV class, which can instead perform efficient Leave-One-Out CV.

https://scikit-learn.org/stable/glossary.html#term-cross-validation-estimator

https://github.com/amueller/talks_odt/blob/master/2015/nyc-open-data-2015-andvanced-sklearn.pdf