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Forced scrolling generally refers to scenarios in 2D games where the player lacks control over the pace that the level proceeds. The screen pans forward past the level, and the player's movement is restricted to within whatever is currently on screen. The related phenomenon in 3D is typically referred to as being “on rails”.
Forced scrolling is the de facto form of movement for most shooters. It simplifies the controls; instead of making you hold down a button to go, it's just automatic. In these cases, it's not just scrolling that's forced, but also ship movement.
Forced scrolling is also often used in platforming games. The airship levels of Super Mario Bros. 3 are a prime example. In these scenarios, the screen crawls past the fixed elements of the level at a constant forward rate, and the player is strictly confined by the bounds of the screen. Generally the task shifts from exploration towards a more “performative” task of avoiding a combination of fixed and moving obstacles. The player must choose between moving forward early, at the risk of running afoul of some not-yet-seen obstacles, or waiting to move later, where he runs the risk of being forced to move by the level's scrolling at moment when the obstacles are more dangerous.
Another variation of forced scrolling is the “crawling doom” scenario, where some deadly, invincible entity chases the player, and the player must race to stay ahead. One example is levels where the player must climb higher and higher to avoid a steadily raising flood of lava. The task here becomes avoiding the obstacles as quickly as possible to stay ahead of and hopefully gain some distance from the pursuing presence.
A third related convention are “moving platform” segments where the player is more or less confined to riding through the level on a platform with no control over its movement. The player is not confined by the screen surrounding the platform, as in strict force scrolling scenarios; rather, the lack of anywhere else to stand forces the player to remain on the platform. This technique is often used for bonus levels, where the level will ends if the player falls off the platform.
“I want to grant the forced scrolling mechanic some noble rationalization; that the invisible wall behind you (pushing you forward) and its partner ahead of you (holding you back) somehow encompass (and thus guide) the playable character's narrative destiny. Why else would it be there? While it doesn't do anything to further determine the character's path (rail shooters are the go-to games for that), it determines the rate at which they can fail and succeed.” – vision.