You're at a restaurant with a group of friends and the waiter has brought the check to your table. You pick up the check, and your friend asks you how much it is. You want to pay for everyone, so you say:
I've got it.
When you're deciding who will pay for a meal, the phrase "I've got it" means "I'll pay for the meal."
In a more general sense, you say "I've got it" when someone is offering to help with something, but you want to show that you can handle the situation without any help. For example, if you're carrying a heavy-looking suitcase and someone offers to carry it for you, you say:
That's all right, I've got it.
(Print this lesson)