A Brute Force attack is an automated process of trial and error used to guess a person’s username, password, credit-card number or cryptographic key.
Many systems will allow the use of weak passwords or cryptographic keys, and users will often choose easy to guess passwords, possibly found in a dictionary. Given this scenario, an attacker would cycle though the dictionary word by word, generating thousands or potentially millions of incorrect guesses searching for the valid password. When a guessed password allows access to the system, the brute force attack has been successful and the attacker is able access the account.
The same trial and error technique is also applicable to guessing encryption keys. When a web site uses a weak or small key size, its possible for an attacker to guess a correct key by testing all possible keys.