In simple terms the logistic regression is a version of multiple regression where the outcome variable is binary (dichotomous), meaning there are only two possible outcomes. The model can be used to calculate the probability of one of the two outcomes occurring over the other for a given case/observation by using the values of a set of known explanatory variables.
This glossary entry refers to a binary logit, the type used in logistic regression. Without getting too technical Logits are basically transformations of existing binary outcome variable data points into a probability P (ranging from 0 to 1). A logit curve is therefore a graph of these logits plotted against an explanatory variable.