Spring arm
A camera boom that holds the camera at a distance behind a target, follows with spring-like smoothing and pulls in automatically when something blocks the view.
A third-person camera can't be bolted rigidly to the character — it would jerk with every step and punch through walls. A spring arm solves both: it attaches the camera to the end of a notional boom and lets it glide smoothly toward the desired pose with spring-like damping rather than teleporting there. The motion feels weighty and cinematic without lagging behind.
The arm also sweeps — usually a shapecast or raycast — from the target toward the camera every frame; if it hits geometry the arm is shortened so the camera pulls in front of the wall instead of ending up behind it. Unreal's USpringArmComponent made the name an industry standard, but the pattern is in nearly every third-person game.