Serial verb constructions are sequences of two or more verbs functioning as a single complex predicate with unified tense/aspect and shared arguments. Common in West African and East Asian languages, SVCs encode meanings that European languages express through adverbial, coordinate, or complex clausal structures.
From your study of syntactic structure and constituency, you know that a canonical clause in English has one main verb whose tense anchors the event and whose argument structure specifies the participants. When you want to describe two events with distinct participants or times, you use two clauses — either coordinated (*She ran and she fell*) or subordinated (*She fell while running*). This one-verb-per-clause tendency is so entrenched in European languages that it can feel like a universal of grammar. Serial verb constructions (SVCs) reveal that it is not.
In a language with SVCs, two or more verbs appear in sequence within a single clause, sharing a single tense/aspect marking and sharing one or more arguments, without any conjunction or subordinator between them. The Ewe sentence from West Africa translating literally as "She take knife cut meat" contains two verbs — *take* and *cut* — but only one tense marking (on the whole construction), one subject (*she*), and a shared direct object (*meat*). English forces you to choose between "*She took a knife and cut the meat*" (two coordinate clauses) or "*She used a knife to cut the meat*" (infinitive complement), each of which packages the information differently. The SVC treats the taking and cutting as a single integrated event, not two sequential ones.
From your typology prerequisite, you know that languages vary systematically in how they encode motion and manner. SVCs are a major typological mechanism for encoding complex events without grammatical subordination. They appear extensively in Kwa languages (Ewe, Akan, Yoruba), Niger-Congo languages, and many Southeast Asian and East Asian languages including Mandarin, Vietnamese, and Cantonese. In Mandarin, the construction *ta pao-chu qu* ("he run-exit go") packs motion, path, and direction into a verbal sequence where English would require an adverbial or prepositional phrase. The three verbs share a single subject and are temporally ordered within the event, but there is no coordinator and no separate tense for each.
The syntactic analysis of SVCs is contested precisely because they challenge the constituency assumptions you studied. Are the verbs each heads of their own VP, projecting separate predicate structures that happen to merge? Or do they form a single complex predicate with one VP? The key diagnostic is argument sharing: in a true SVC, the object of V1 is the subject of V2 (*She took the knife cut the meat* — *knife* is what she took and also what cut the meat, as an instrument). This shared argument structure with no overt connective is what distinguishes SVCs from simple coordination and from causative or purposive complements, which have their own structural signatures. Resolving the constituency question forces syntacticians to reconsider which features — shared tense, shared arguments, absence of conjunction — are definitional to clause-hood itself.