In more detail
The name comes from the fairy tale of Hansel and Gretel, who left a trail of crumbs to find their way home. On a website, breadcrumbs show the path from the home page to the current page, with each level clickable.
Breadcrumbs do two jobs for SEO. First, they add consistent internal links up the hierarchy, which helps search engines understand how pages relate and helps link value flow to category pages. Second, they can be described with BreadcrumbList structured data. Google's breadcrumb documentation explains that it uses this markup to categorise information from the page in search results.
Breadcrumbs work best when they reflect a logical structure, such as category › subcategory › product, rather than the visitor's browsing history. On large ecommerce sites they are especially useful because products often sit several levels deep. If a product belongs to several categories, pick one primary path for the breadcrumb so the structure stays consistent.
Why it matters when hiring an agency
Breadcrumbs are usually a template change, so they are cheap to add and affect every page at once. They're a good example of the kind of structural improvement a technical SEO audit should identify.
If an agency recommends them, ask for the proposed hierarchy, not just the markup. The structure matters more than the code: a clear category system benefits navigation, internal linking and reporting. Also ask the agency to validate any structured data with Google's Rich Results Test, and to make sure the markup matches what visitors see on the page, as Google's structured data policies require.