Vertical integration is when a company buys another business in the same supply chain. If a grocery store corporation purchases a factory that produces canned goods, which it then sells in its stores, that's vertical integration.
Economists talk about vertical integration when they're discussing the merging of businesses at two different stages of production (such as making things and selling them). Vertical integration occurs when one company buys or merges with another and the result is more control over the process of producing things, distributing them, and selling them to customers. Next time you see a store brand product at a big box store, you can say, "Vertical integration!"