The fitted value is also called the event probability or predicted probability. Event probability is the chance that a specific outcome or event occurs. The event probability estimates the likelihood of an event occurring, such as drawing an ace from a deck of cards or manufacturing a non-conforming part. The probability of an event ranges from 0 (impossible) to 1 (certain).
In binary logistic regression, a response variable has only two possible values, such as the presence or absence of a particular disease. The event probability is the likelihood that the response for a given factor or covariate pattern is 1 for an event (for example, the likelihood that a woman over 50 will develop type-2 diabetes).
Each performance in an experiment is called a trial. For example, if you flip a coin 10 times and record the number of heads, you perform 10 trials of the experiment. If the trials are independent and equally likely, you can estimate the event probability by dividing the number of events by the total number of trials. For example, if you flip 6 heads out of 10 coin tosses, the estimated probability of the event (flipping heads) is:
Number of events ÷ Number of trials = 6 ÷ 10 = 0.6