"[someone / something] has / has got you covered." Has two similar meanings: 1) it means that [someone / something] has all the resources or information you need for a particular situation, or 2) that you can rely on [someone / something] to support you with money or help. You will often hear the first meaning in adverts: "Have a new dog in the house? Pets Superstore has you covered" (Pets superstore has everything for dogs) "Learning a foreign language and need a conversation partner? italki has got you covered" (italki has everything you need to find a conversation partner) "Need an idea for a unique wedding present? newlyweds.com has you covered" (newlyweds.com has everything you need to buy a unique wedding gift) The second meaning you might hear between friends: "Don't worry about paying for drinks, I've got you covered" (I will pay for your drinks) "You don't need to explain to our parents, I've got you covered" (I will explain to our parents) You could correctly change the object of the sentence: "[someone / something] has / has got [someone / something] covered." "We don't need to pay for his travel, his work has got him covered" But 95% of times it is used with "you".

Let me try explaining it without using grammatical names, but simply by giving some examples of other sentences that are similar and which look more 'normal': I have roses in my garden. I have you in my garden. I have roses under glass. I have you under control. I have my roses well watered. I have you well cared for. I have my roses covered. I have you covered. Note that for a speaker of British English the preferred form for your original sentence would be "I've got.you covered". If this still doesn't make sense, at least we now have some more examples to work with and can focus more specifically on your problem.

You are covered like an umbrella covers you, or a coat covers and protects you. It is a word picture to express protection or care using insurance or a promise. Eg i will cover your expenses = i promise to protect you from.....costs.