The Short Version
Breadcrumbs show a "trail" of pages or categories through which a website's visitor has navigated to reach the current page.
The Detailed Version
Breadcrumbs is the name given to a type of website navigation whereby the current page location can be seen easily in relation to the site's overall structure. Breadcrumbs create a visible, recursive path.
The following example of a breadcrumbs trail might be found at an online retailer's site:
Home > Accessories > Purses and Wallets > The New York Money Clip
In this example, the individual may have begun at the site's home page, clicked on the Accessories page, clicked on the Purses and Wallets sub-page, and then clicked on the product page for the New York Money Clip item.
It's also possible that the visitor linked directly to the product page from an advertisement online without starting at one of the previous pages in that site's hierarchy. If the site features breadcrumbs, though, the trail will still be displayed on the page. If the visitor did in fact link directly to this page from somewhere else, he or she could use the breadcrumbs trail to see at a glance where in the site they are.
Additionally, the visitor can back up through the site's hierarchy step-by-step by clicking on the breadcrumbs trail in reverse order. In the example above, this would be useful if the visitor decided the New York Money Clip wasn't the right product, and instead of shopping for a wallet, wanted to browse belts. He or she could click on Accessories in the breadcrumbs.