In modern finance, it's standard practice for service providers like banks to retain custody of your assets. This means that when you want to make a withdrawal from your bank account for example, while you may have a legal claim to the money, the reality is that you're asking for permission from your bank. Banks can and regularly do deny such permission, and their reasons for doing so do not always align with the best interests of individual customers. Further, even when service providers uphold the custody rights of their customers in good faith, factors outside of their control may force them to deny you access to your money. For example, a government may force banks to restrict withdrawals in an attempt to stop runaway inflation, as happened in Greece in 2015. Another, perhaps more insidious example, is Operation Choke Point, where the US government pressured banks to deny service to people involved in a variety of (legal) industries it had identified as morally corrupt.
With the advent of decentralized systems - of which Bitcoin is the primary example - it became possible, for the first time, to provide non-custodial financial services at a large scale. In the non-custodial model, the customer retains full custody (possession) of their assets at all times, using the service provider merely as an interface for conveniently managing their assets.
When you install a non-custodial Bitcoin wallet (like the Bitcoin.com Wallet), first of all, you don't need to ask for permission to use the service. There's no account approval process, meaning anyone in the world can download the app and start using it immediately. Secondly, only you have access to your funds. This makes it nearly impossible for the service provider (in our case Bitcoin.com), a government, or anyone else to prevent you from using your funds exactly as you wish.
Of course, with great power comes great responsibility. Since you're the only one with access to your funds, you need to manage your wallet carefully. This includes backing up your wallet and adhering to password management best practices.
Absolutely not. Centralized cryptocurrency exchanges like Coinbase, Binance, and the Bitcoin.com Exchange provide custodial Bitcoin wallets (sometimes known as 'web wallets'). While such exchanges are useful for buying, selling, and trading bitcoin into a wide variety of other digital assets, when you use these exchanges, your bitcoin is held in trust by the exchange.
The risks are similar to (and in many cases greater than) those associated with holding your money at a bank or using a payment app like PayPal. The risks stem from the fact that, fundamentally, you're not in full control of your funds.
Firstly, since taking custody of financial assets is a regulated activity, centralized cryptocurrency exchanges are subject to the whims of regulators in the jurisdiction they are domiciled. This means there's always the possibility that you'll wake up to find you are unable to access your bitcoin. Secondly, the exchange may charge extra fees for withdrawals (which is common), slow down your withdrawal process (also common), or prevent you from withdrawing altogether (rare but not impossible). Finally, there's always the risk that the exchange will go bankrupt, get hacked, or intentially dissolve - and since cryptocurrency exchanges generally aren't insured and are often registered offshore, it's likely you'll lose your bitcoin and have no recourse to action.
All non-custodial Bitcoin wallets enable you (and only you) to possess the private key associated with your public Bitcoin address. This typically takes the form of either a file or a mnemonic phrase that consists of 12-24 randomly generated words. If your Bitcoin wallet doesn't have this option, it's custodial (meaning you're not in full control of your bitcoin).
The Bitcoin.com Wallet, which is fully non-custodial, also offers a Cloud Backup service (in addition to giving you the option to store your private key as a mnemonic phrase). Here, you create a single custom password that decrypts a file stored in your Google Drive or Apple iCloud account. If you lose access to your device, simply reinstall the Wallet app on a new device, enter your password, and you'll again have access to all of your bitcoin (and all other digital assets in your wallet). Further, whenever you add more wallets within your Bitcoin.com Wallet, your backup file will automatically sync. This means you never have to worry about creating a new backup for each new wallet you create!
Read more: What are the advantages of the Bitcoin.com Wallet Cloud Backup Service?