Definition of search
Search functionality is a part of the product's navigational system. It's an emergency exit that helps users find what they're looking for on a page or the whole website and find their way back if they get stuck in navigation.
Search functionality isn't the only navigational feature. Depending on users' level of knowledge, expertise, and goals, they choose different techniques for finding what they need. For example, visitors of an e-commerce website may browse the catalog, go to their wish lists, and recommendations, or use a search input to find the specific item.
There are a lot of options for implementing search functionality, but the most expected variant is a simple text input wide enough to contain a word or phrase users search for. When they hit "Enter" on their keyboard or click the search button, they should receive a list of results matching their search query.