Local play is a form of multiplayer which does not require any connections to a network or the Internet as it is hosted on one machine. Either all players are visible in one scene (usually 2D games) or the monitor is split into multiple screens (3D games). Players will often require additional input devices to join the game (e.g. a controller).
It is possible for players to use an Internet connection to join each other in this mode. A generalist third-party tool like Parsec can be used to achieve this, while some games on the Steam storefront have the Remote Play Together feature which does this natively.