Public Key & Private Key
A private key is a secret number that controls your funds; the public key is derived from it and can be shared safely.
In depth
Think of the public key as your account number and the private key as the signature that authorises withdrawals — except this signature cannot be forged. The maths lets anyone confirm a signature came from the private key without ever seeing that key. Whoever holds the private key controls the coins, full stop.
Why it matters
"Not your keys, not your coins" — every wallet, exchange account and hack story comes down to who holds the private key.