As a user of a cryptocurrency wallet, you don't necessarily need to understand the precise details of BIP39 calculations. However, you might want to understand that they include the generation of a checksum of random numbers, and this is used as an integrity check. A checksum is a small piece of data that allows you to check if another piece of data is the same as expected. This checksum is included in the last mnemonic code word of a sequence, and it helps wallets to verify the validity of every mnemonic sentence. So if a user types in a set of words and it fails validation because the checksum isn't as expected, there is likely a typo in what the user entered. BIP39's other mathematical functions transform its inputs (the random numbers plus the optional passphrase) through one-way functions that guarantee that they can not be reverse-engineered from the public key. If you'd like to do a deep dive, and understand the exact mechanisms of how BIP39 wallets convert mnemonic codes into a binary seed, there is a description in the design document at https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki. Vault12 also has a more detailed description in "How to Generate a Seed Phrase."