There are two primary purposes of a "controlled round feed" system. First is as has been stated, to control the cartridge from the magazine to the chamber. Many Remmy 700's will reliably feed upside down and/or sideways, but that's only the first part.
The German army also wanted a feature such that the rifle would not double feed and jamb if short stroked. If a push feed rifle round is not fully chambered, the extractor does not grab the rim, and cannot extract it. If the bolt is retracted again (because the soldier in fear of his life forgot he already (almost) cycled the action once), another cartridge is stripped from the magazine, and shoved into the back of the first one. If it happens just wrong, the rear bullet can strike the front cartridge's primer, causing an out of battery ignition (very bad). Even if it does not cause out of battery ignition, it is a tricky (in the heat of battle) situation to clear, since the loose rear cartridge is not aligned with the bolt/extractor, and cannot be ejected from the action. One has to partially retract the bolt (not far enough to strip another round, but far enough to open the action for the rear cartridge to fall out), then turn the rifle on its side to dump out the rear cartridge. Then, without retracting the bolt any further, close the bolt on the forward cartridge (in the chamber) where it can be fired or extracted/ejected as normal.
Since controlled round rifles have the cartridge captive on the bolt face from the moment they leave the magazine, this double-feeding situation cannot happen no matter what the soldier does (or doesn't) do in the heat of battle.
Andy