What do we learn from training a dataset for logistic regression
I hope this is what you are looking for:

In Linear regression, the parameters are learned (e.g. theta1,theta2, etc.) which are then used to help us in predicting the real value ( as it is the regression problem)
But In case of logistics regression (as it is used for classification purposes) the same parameters are learned but different activation function is used like sigmoid which results in the range of 0 to 1( which actually shows the probability of an outcome). So, based on your requirement, if the result of the sigmoid or any other activation function crosses a certain threshold value which can be any between 0 to 1, then it is classified as one class otherwise the other class.

For example, If after multiplying all the parameters and input values and then applying activation function on the multiplication result, the output value is 0.7 which let say is great than our threshold value(e.g. 0.5) then it is classified as YES otherwise NO.