What is log likelihood in logistic regression?

It is the sum of the likelihood residuals. At record level, the natural log of the error (residual) is calculated for each record, multiplied by minus one, and those values are totaled. That total is then used as the basis for deviance (2 x ll) and likelihood (exp(ll)).

The same calculation can be applied to a naive model that assumes absolutely no predictive power, and a saturated model assuming perfect predictions.

The likelihood values are used to compare different models, while the deviances (test, naive, and saturated) can be used to determine the predictive power and accuracy. Logistic regression accuracy of the model will always be 100 percent for the development data set, but that is not the case once a model is applied to another data set.