The term cryptocurrency wallet can initially be confusing to some people because they believe it contains their coins. However a cryptocurrency wallet is quite simply where you store your private keys. There are two types of wallet that differ depending on if the keys are related to each other, these are deterministic and non-deterministic wallets.
The more traditional approach to wallets was called non-deterministic wallets. These wallets came with randomly generated private keys and were able to generate further random keys when requested. Whilst at the outset from a security perspective this sounds a positive thing, none of the keys having a relationship to each other creates a management headache. Since there is no relationship between any of the keys each and every key must be backed up. As you generate more and more keys the management challenge increases.
More modern wallets are called deterministic wallets. In these deterministic wallets all the private keys are related back to a seed. A one-way hash function is applied to the seed to generate all of the private keys. Anyone that has setup a Ledger Nano S will have been through the process of creating the seed without even realising it. When you setup a ledger Nano it displays 24 words in turn on the screen and you are prompted to make a note of each in order. This is very important since these are your seed phrases. And herein lies the major advantage of deterministic wallets, should you lose your Ledger Nano or other deterministic wallet you would simply input your mnemonic seed words to recover your keys. This single backup of your seed words provides considerably improved simplicity compared to having to backup every single key separately as with a non-deterministic wallets.
The 24 seed words you provide to your Nano are called mnemonic codewords or passphrase. The mnemonic phrases are established by the BIP-39 standard.
Some deterministic wallets take the idea of creating multiple keys from a seed even further. Systems supporting the BIP-32 are called hierarchical deterministic wallets or HD wallets and standard child keys can spawn further grandchildren keys and so on, as shown in the top image. This kind of hierarchical keys would be useful to a corporation spending cryptocurrency, since they would be able to allocate certain departments and functions to the various sub trees in order to track expenses. Examples of wallets supporting BIP 32 include the Ledger Nano S and Trezor to find the most suitable wallet for your cryptocurrency take out wallet chooser wizard for a spin.