The mnemonic seed is a sequence or a word scheme that helps the brain remember more complicated things. An example of mnemonic seed phrase; "May I have a large container of coffee beans" in English (may I have a large container of coffee beans). This sentence represents Pi, each letter corresponding to the position of each 3.14159265 decimal place. The mnemonic seed words in cryptocurrency is a little more complicated, but the concept is the same.
A private key is hard to recall. Most wallets generate a 24-word seed phrase which represents your root seed in a much simpler format. The words are common English words such as mountain and biking.
When you set up your wallet for the first time, you will need to note the seed words carefully. Write them down on paper and break it into two sections. As long as you have access to both pieces of paper, your keys are secure in case you lose access to your wallet.
When storing cryptocurrencies on an exchange, your private keys are not in your control. Your funds are not yours. The famous phrase: "Not your keys, not your coin." Storing cryptocurrency on an exchange is exposing yourself to hacks. They store your private keys on their servers.
A hardware wallet (e.g. Nano Ledger) protects your keys and addresses under a secure layer of software and hardware. So, you are regaining control over your cryptocurrencies. The hardware wallet randomly generates mnemonic seed words. So we suggest that you copy this words/sentence into a protected medium when initializing your hardware wallet. We do not recommend that you store it online on a cloud service.
Thank you for learning with me and hope you have a good rest of the day!