A browser extension is an application that lives in your browser and can be injected into websites and dApps, allowing you to interact with them. The most common browser extensions in the crypto world are light wallets that allow users to interact with dApps such as NFT marketplaces and other blockchain based websites and dApps.
Other things such as ad-blockers and coupon applications are also browser extensions. Browser extensions are often located in the top right hand corner of your browser, inline with the search bar.