One way to own your private key is to actually download it to your device. You install your wallet on your computer. These types of wallet is called desktop wallet. You can access a desktop wallet only from the single computer you downloaded it. Your private key is not on a central server, it is stored locally on your computer. This means you have all the responsibility. If you lose your private key there will be no customer support to help you access your fund. Always be safe by backing up your private key in case your device gets stolen or broken. See "What is a seed?" article.
As long as your device is free of malware and virus your fund is safe. But you never know what kind of malware programmes are running on your device without your knowledge. As these malwares are silent and activate only when you use your wallet. When a virus recognises your wallet, it screenshots your private key and sends it to a malicious hacker who will be able to access your fund. Viruses and malwares are much more common on computers than on mobile phones. This is why we recommend not to use desktop wallets.