Cryptography
The secret value that decides how data is scrambled and restored - whoever holds it can read the protected data.
Formal
A long, randomly chosen value fed into an encryption or signing method. The method itself is public, so all of the protection rests on keeping the right key secret and on it being too long to guess.
In plain English
Like the key to a padlock - everyone knows how padlocks work, but only the person with the right key can open this one.
In practice
The IT operations lead at a pension fund keeps the keys for its encrypted backups in a separate, locked-down system, so an attacker who gets hold of the backups does not also get the keys.
Why it matters
Encryption is only as strong as the care taken with its keys; a lost key means lost data, and a leaked key means no protection at all.