As explained in a [comment][1]: **A generic attack is one that works against all block-ciphers (with a given block and key size), without consideration about the structure of the block-cipher**.

One generic attack for a block cipher of a given block size $b$ bits builds a _dictionary_ of input/output pairs (e.g. from past plaintext/ciphertext), for a fixed key. When an input or output in that dictionary gets reused, the adversary gains an advantage. In many scenarios, that's expected after about $2^{b/2}$ blocks (less in ECB mode, more in CTR mode). Such attack works for any block cipher, including an hypothetical one implemented as a random permutation.

If we in addition consider the key size of $k$ bits, another generic attack, _brute force key search_, enumerates the keys. With at least $k/b+1$ input/output pairs, that's likely to find the key after about $2^{k-1}$ attempts.

Sometime we have a generic attack against a whole category of block ciphers sharing a common characteristic. For example, there's a generic attack against all [Feistel ciphers][2], based on the fact that for any key, they implement an [even permutation][3]; this allows an adversary having built a dictionary of all input/output pairs except two of these, to deduce the remaining two with certainty. Another example (given in that [answer][4]) is an enhanced brute force key search removing most of the work associated to the first and/or last round in a Feistel cipher.


  [1]: http://crypto.stackexchange.com/questions/14547/block-ciphers-and-non-generic-attacks#comment29428_14547
  [2]: http://en.wikipedia.org/wiki/Feistel_cipher
  [3]: http://en.wikipedia.org/wiki/Parity_of_a_permutation
  [4]: http://crypto.stackexchange.com/a/14549/555