Metathesis is a phonological process in which two segments exchange positions within a word or phrase. It can be sporadic (lexically-specific), regular (phonologically conditioned), and is often motivated by repair of illicit sequences or vowel-consonant reordering constraints.
From your study of phonological rules and derivation, you know that phonological processes alter segments in systematic ways — assimilation makes sounds more alike, deletion removes segments, insertion adds them. Metathesis is a different kind of operation: rather than changing a segment's features, it reorders two segments, swapping their positions within a word. The segments themselves stay intact; only where they sit in the sequence changes.
The most familiar English example is the word "ask," which many speakers produce as "aks" — swapping the /s/ and /k/. This is often stigmatized as a modern error, but it is in fact ancient: Old English had both "ascian" and "acsian" as variants, and the metathesized form has continuous attestation across centuries of English dialects. Another common example is "nuclear" pronounced as "nucular" — the /l/ and the following vowel exchange positions. Historical linguistics is full of such cases: the Latin word "parabola" (a speech, a parable) metathesized into Spanish "palabra" (word) through a complex vowel-consonant reordering over several centuries.
Why does metathesis happen? The primary motivation is often repair of phonotactically difficult sequences. Every language has constraints on what sequences of sounds are permitted within a syllable or word boundary. When a sequence arises through borrowing, morphological combination, or historical change that violates these constraints, speakers may reorder sounds to produce a more acceptable structure. Consonant clusters at syllable edges are a common target: if a language prefers open syllables (CV rather than CVC or CCV), a cluster like /sk/ at the end of a syllable might be repaired by metathesis into a more permissible arrangement.
The distinction between sporadic and regular metathesis maps directly onto the framework you already know from phonological rules. Sporadic metathesis affects specific lexical items without a phonological conditioning environment — the /sk/ → /ks/ swap in "ask" happens to that word (and a few others), not to every /sk/ sequence in English. Regular metathesis, by contrast, is phonologically conditioned: it applies systematically whenever a certain feature combination or phonological context is present, and can therefore be written as a proper phonological rule. Rotuman (a Polynesian language) exhibits regular CV metathesis as part of its morphological system — the same metathesis operation applies predictably to mark a grammatical category across thousands of words. Recognizing this sporadic/regular distinction allows you to diagnose whether a case of metathesis requires a lexical entry annotation or a productive phonological rule.