Networking
Scrambling data with a secret key so only someone holding the matching key can read it.
Formal
A mathematical process that uses a key to transform readable data into a form that cannot be read, such that only a holder of the matching key can turn it back. The key may be shared by both sides (symmetric) or split into a public and a private part.
In plain English
Like writing a letter in a secret code only you and a friend know - anyone who steals the letter sees only gibberish.
In practice
A nurse in a municipality's home care leaves her work laptop on the bus; its disk is encrypted, so whoever finds it cannot read the citizens' care notes without her password.
Why it matters
Data is copied, lost and overheard all the time; with encryption a stolen disk or tapped connection reveals nothing readable, which can turn a serious data breach into a minor incident - as long as the key stays safe.