ADA is always kept on the Cardano blockchain in an encrypted entity, which is called a “blockchain wallet”. A wallet on the blockchain can be accessed through different  interfaces, we will refer to them here as “software wallets”. A private cryptographic key is needed to access a wallet on the blockchain. 

When you buy ADA on a cryptocurrency exchange, a blockchain wallet is automatically created for you and ADA is stored in it. Exchange, however, is not giving you the access to the private keys, but instead it is just ensuring that a person with an access to the exchange account, will be able to manage funds in the blockchain wallet.

There is a popular saying “not your keys = not your wallet”. It means that nevertheless exchange is enabling you to manage the Cardano funds in the blockchain wallet, this access is dependent on that exchange, a third-party. Whilst this can be convenient, there are two good reasons to trouble yourself to hold your ADA in your own blockchain wallet, accessed through software wallet.

— First, your cryptocurrency exchange account is accessed through their server, which means it is accessible for hacking attempts 24/7. If this happens, there is not assurance that exchange will be intending to compensate the losses.
— Second, having ADA on exchange, you will not be able to access advanced features, such as lock-free staking, voting and others.