This consists of simply going through every possible key, deciphering the ciphertext with each key, and trying to find some recognizable cleartext in the result. If you use a 128-bit key there are 2128 possible keys.
A would-be code-breaker would regard this type of attack as the last resort, to be used only if there is no feature - that is, weakness - of the cipher that makes possible some more intelligent attack. A cipher that forces the code-breaker to resort to this method is a strong cipher.
However, ciphers that use weak (small) keys are susceptible to brute force attack, in particular RC4-40, RC2-40 and DES-56. There have been many successful brute force attacks against RC4-40 since its release in February 1995.
A brute force attack against ciphers with 128 bits or more is probably impractical in the foreseeable future.