A browser engine is the portion of browser that works under the hood to fetch a web page from the internet and translate its contents into forms you can read, watch, hear etc
A browser engine includes many sub-components: an HTTP client, an HTML Parser, a CSS parser, a Javascript engine(composed of parsers, interpreters and compilers). These components involve in parsing web formats like HTML, CSS and translating them into what you see on-screen are sometimes called layout engine/rendering engine