Consonant harmony is a type of "long-distance" phonological assimilation akin to the similar assimilatory process involving vowels, i.e. vowel harmony.
A good discussion of consonant harmony typology is found in Rose and Walker's 2004 paper in the journal Language, "A Typology of Consonant Agreement as Correspondence."
One of the more common harmony processes is coronal harmony, which affects coronal fricatives, such as s and sh. Then, all coronal fricatives belong to the +anterior class (s-like sounds) or the -anterior class (sh-like sounds). Such patterns are found in the Dene (Athabaskan) languages such as Navajo (Young and Morgan 1987, McDonough 2003), Tahltan (Shaw 1991), Western Apache, and in Chumash on the California coast (Applegate 1972, Campbell 1997). In Tahltan, Shaw showed that coronal harmony affects three coronal fricatives, s, sh and the interdental th. The following examples are given by de Reuse: in Western Apache, the verbal prefix si- is an alveolar fricative, as in the following forms:
However, when the prefix si- occurs before a verb stem that contains a post-alveolar affricate, the si- surfaces as the post-alveolar shi-:
Thus, all sibilant obstruents (fricatives and affricates) in these languages are divided into two groups, +anterior (s, ts, dz) and -anterior (sh, ch, j). In Navajo, as in most languages with consonant harmony, there is a constraint on the shape of roots (a well-formedness constraint) that is identical to the harmony process. All roots with sibiliant affricates or fricatives have the same value for anteriority. Shaw (1991) provides a phonological analysis of this process, using data from research on Tahltan.