Keys with an exploitable mathematical relationship, and the attacks they enable
Related keys are pairs or larger sets of keys which have an exploitable mathematical relationship for a given cipher. This relationship can be simple, such as differing in a few bits (like equivalent keys in TEA), or it can be more complex (like related-key boomerang attacks against the AES key schedule).
Related-key attacks are typically only an issue for ciphers (stream or block) used in woefully-incompetent protocols, or when a block cipher is used as the building block for a hash function. As such, many new cipher constructions do not consider related-key attacks to be a major threat.