You are familiar with passwords, your secret login credentials. Passphrases are longer, full 'phrases' that add security while often being easier to remember.
Because a passphrase is longer, you don't need to worry about adding numbers, symbols, and mixed-case letters to make it strong. A few random lower-case words will be relatively easy to remember, while substantially increasing your account's security.
When you sign up, Peerio will automatically generate a passphrase for you.
Peerio defaults to six-word passphrases to achieve an estimated 80-bits of entropy, which is estimated to cost about about $1B (US) to crack in a year. Peerio also uses scrypt to make cracking even more costly in both time and money.
For even greater security, you can choose to use a passphrase with up to 10-words — where each additional word adds an estimated 13-bits of entropy.
If you don't like the passphrase given, you can click the "Change passphrase" button to generate new passphrases until you find one you like.
It is important to remember your passphrase, write it down on a sheet of paper and store it securely. If you lose your passphrase, you lose your account!
If you are still a bit confused about why we use passphrases, this comic from xkcd explains the issue excellently: