Their importance is in the name. Private keys are unique to your wallet. Without them, no one can access your wallet (unless your password is weak). By generating and holding them, you are able to recover your wallet and/or claim any coins that resulted from a fork e.g. bitcoin cash.
You might find yourself in a position when you’re not holding your private keys by storing your coins on an exchange wallet. While this is great for having your account funded and ready to trade, it is not a sustainable long-term solution.
Majority of projects have developed desktop, mobile or hosted wallets for their coins. Bitcoin wallets like blockchain’s allow you to hold your private keys while being user-friendly. Cold storage wallets like Trezor and Ledger are also great for security, convenience and the range of coins that you can hold there at once.