You have a house. You have a key to your house. Your key to your house is owned by the exchange. The exchange gives you the key so you can enter your house. If the exchange disappears your key will disappear with them and you can no longer enter your house.

BUT

Some wallets (mostly offline ones) let you have your own keys owned by you alone and you can use these keys to enter your house any time you want. You can import these keys into other wallets which will let you into your house (coins).

Now apply this example to your coins