Let’s get the technical explanation out of the way first: A transverse engine is an engine mounted horizontally in the engine bay so that the engine’s crankshaft axis is perpendicular to the direction of the vehicle’s travel. Conversely, longitudinal engine crankshafts are positioned parallel with a car’s direction of travel.
The non-technical way of explaining transverse and longitudinal engine mounting is that the shaft poking out of the engine and spinning really fast (crankshaft) can be pointed towards the back of the car (longitudinally) or to one side of the car (transversely). A common drivetrain layout using a longitudinally-mounted setup is a front-engine, rear-wheel-drive car. That allows the crankshaft to be connected to a drive shaft that runs the length of the chassis, connecting to the rear differential and powering the rear wheels. A front-wheel-drive car doesn’t need a driveshaft like that, so they usually use a transverse-mounted engine.
Typically, a front-engined, rear-wheel-drive car is a more performance-oriented layout and used in sporty, premium, or luxury cars. Front-wheel-drive has long been the less expensive layout, hence the rarity of front-mounted transverse V8 engines.