Weak keys are secret keys with a certain value for which the block cipher in question will exhibit certain regularities in encryption or, in other cases, a poor level of encryption. For instance, with DES (see Question 64) there are four keys for which encryption is exactly the same as decryption. This means that if one were to encrypt twice with one of these weak keys, then the original plaintext would be recovered. For IDEA (see Question 77) there is a class of keys for which cryptanalysis is greatly facilitated and the key can be recovered. However, in both these cases, the number of weak keys is such a small fraction of all possible keys that the chance of picking one at random is exceptionally slight. In such cases, they pose no significant threat to the security of the block cipher when used for encryption.
Of course for other block ciphers, there might well be a large set of weak keys (perhaps even with the weakness exhibiting itself in a different way) for which the chance of picking a weak key is too large for comfort. In such a case, the presence of weak keys would have an obvious impact on the security of the block cipher.