Blockchains are secure by design and are an example of a distributed computing system with high Byzantine fault tolerance. Decentralized consensus has therefore been achieved with a blockchain. Blockchains solve the double-spending problem without the need of a trusted authority or central server, assuming no 51% attack (that has worked against several cryptocurrencies).
Within a cryptocurrency network, only miners can confirm transactions by solving a cryptographic puzzle. They take transactions, mark them as legitimate and spread them across the network. Afterwards, every node of the network adds it to its database. Once the transaction is confirmed it becomes unforgeable and irreversible and a miner receives a reward, plus the transaction fees.
Essentially, if you are interested in trading in digital currencies but don't want to get bogged down in the underlying technology, products like Coinbase are a way to begin a foray into a new form of currency speculation and investing. You do, however, lose some of the advantages of trading in a cryptocurrency and through the blockchain. On Coinbase, you have no pseudo anonymity—your name is attached to your Coinbase account and so is your bank account, so transaction history is relatively easy to track down. And if you're not working on the blockchain, there's not much you can do to ensure that the verification of your transaction history or your account is taking place on the blockchain. You are, instead, placing trust in the intermediary, in this case, Coinbase.
If you do have this much money tied up in Bitcoin, though, you may want a more secure space to store it. If this is the case, Coinbase offers a Coinbase vault, which has time-delayed withdrawals (giving you 48 hours to cancel a withdrawal) and the option of multiple approvers, increasing security by ensuring that all withdrawals are approved by multiple people. They also offer a multisig vault, which is basically an even more involved and more secure vault, requiring multiple keys to unlock.
On 21 November 2017, the Tether cryptocurrency announced they were hacked, losing $31 million in USDT from their primary wallet. The company has 'tagged' the stolen currency, hoping to 'lock' them in the hacker's wallet (making them unspendable). Tether indicates that it is building a new core for its primary wallet in response to the attack in order to prevent the stolen coins from being used.