When the e.dentifier is connected to your computer, the e.dentifier screen will give you information about the action you are performing (logging in or making a payment) or the payment (number of payments and total amount). You can see precisely what is happening.
In other words, in the connected mode, the payments shown on your computer screen are confirmed on the screen of the e.dentifier. This provides an additional check which makes it more difficult for fraudsters to mislead you. That's because installing fraudulent software on both your computer and the e.dentifier is highly complicated.
Using the e.dentifier in connected mode also makes things simpler: you only need to enter codes once rather than having to do so for each payment. That's especially useful when you are making lots of payments at the same time.