Flinging is a basic movement skill in both Portal and Portal 2, in which the player converts a downwards kinetic energy from gravity of either himself or an object, to the same energy directed straight up, horizontally or diagonally. This skill is performed by placing a portal on a surface far below the the player, and another portal facing the intended direction of movement. The player then falls into the first portal, accelerating due to gravity. As momentum is conserved between portals, the player is then "flung" out of the second portal at the velocity they reached accelerating downwards.
However, there are major differences in how these are handled in each game.
In Portal, the player can literally bend their flying arc sideways during a fling, about the same way the Demoman or the Soldier do in Team Fortress 2. In Portal 2, there is little to no air control; it is kept to a slight bending, and can be predicted accurately, or be a result of a prediction.
In Portal 2, it is no longer possible to crouch-jump into a portal, entering into a portal crouched makes no difference. In Portal, it is possible to enter a floor portal diagonally while crouched to perform special flings, and to fling crouched to reach higher places. In Portal 2, crouching doesn't make a difference, but flinging diagonally is still a possible move if the portal is placed on a diagonal surface, or if the player enters the portal diagonally.
Portal 2 introduces the Aerial Faith Plate, which acts similarly to a fling, using a trigger_catapult instead of a pair of portals. It is used extensively in places in which the level designer wants to make the player land on a small area, keeping the 'random factor' deaths to a minimum. Debugging tools are available in Portal 2 (through the ent_bbox and ent_absbox commands) to visualize predicted flinging arcs from a trigger_catapult.
Props like cubes are handled differently in Portal and in Portal 2. In Portal, it uses about the same system as the gravity gun as the handled prop keeps a lot of its physical properties. In Portal 2, some of the physical properties of the handled prop are sacrificed to allow the player to fling with those props without too much of a problem.