A seed phrase, seed recovery phrase or backup seed phrase is a list of words which correspond to the master private key of a Bitcoin SV wallet. In typical usage, a wallet will generate a seed phrase and instruct the user to write it down on paper. If the user's computer breaks or their hard drive becomes corrupted, they can download the same wallet software again and use the paper backup to deterministically re-generate their wallet. Seed phrases are the most frequently encountered means of backing up Bitcoin SV wallets.
Anybody with access to the phrase can steal the bitcoins, so it must be kept safe. Phrases should not be transmitted electronically and should never be written on any website.
An example of a seed phrase is:
witch collapse practice feed shame open despair creek road again ice least
The word order is important.
A simplified explanation of how seed phrases work is that the wallet software has a list of words taken from a dictionary, with each word assigned to a number. The words in the seed phrase are each converted to their corresponding number and concatenated to generate the seed integer to a deterministic wallet. From this seed integer the wallet generates all key pairs used in the wallet.
The English-language wordlist for the BIP39 standard has 2048 words, so if the phrase contained only 12 random words, the number of possible combinations would be 2048^12 = 2^132 and the phrase would have 132 bits of security. However, some of the data in a BIP39 phrase is not random (see: BIP39: Generating the mnemonic), so the actual security of a 12-word BIP39 seed phrase is only 128 bits.
Two-Factor Seed Phrases
Several wallets enable their users to generate seed phrases with an added layer of encryption to prevent someone who discovers the words from accessing the wallet. The password can be used to create a two-factor seed phrase where both "something you have" plus "something you know" is required to recover the wallet.
This works by the wallet creating a seed phrase and asking the user for a password. Then both the seed phrase and extra word are required to recover the wallet. ElectrumSV and some other wallets call the passphrase a "seed extension", "extension word" or "13th/25th word". The BIP39 standard defines a way of passphrase-protecting a seed phrase. A similar scheme is also used in the Electrum SV standard. If a passphrase is not present, an empty string "" is used instead.
Storing Seed Phrases for the Long Term
Most people write down phrases on paper but they can be stored in many other ways such as memorising, engraving on metal, writing in the margins of a book or any other creative and inventive way.
For storing on paper, writing with pencil is much better than pen Pencil Does Not Fade How do I maintain a paper notebook that can remain for years?. Paper should be acid-free or archival paper, and stored in the dark avoiding extremes of heat and moisture Essential facts about preservation of Paper Writing in a notebook with pencil CoPAR: Creating records that will last .
Generally a seed phrase only works with the same wallet software that created it. If storing for a long period of time it's a good idea to write the name of the wallet too.
The BIP39 English word list has each word being uniquely identified by the first four letters, which can be useful when space to write them is scarce.
Alternative name "Mnemonic Phrase"
Seed phrases are sometimes called "mnemonic phrases" especially in older literature. This is a bad name because the word mnemonic implies that the phrase should be memorised. It is less misleading to call them seed phrases.
The power of backups
An especially interesting aspect in the power of paper backups is allowing your money to be in two places at once. You can store backups on multiple devices/physical media in different locations and with password encryption. With that, you can carry $100,000 which can instantly be moved to a phone or transferred with total security. If it's stolen, then there is no risk because it is backed up elsewhere. 
This content is based on content sourced from https://en.bitcoin.it/wiki/Seed_phrase under Creative Commons Attribution 3.0. Although it may have been extensively revised and updated, we acknowledge the original authors.