When you press the right bumper to reload your current weapon, you can press the right bumper again when the pointer is along the grey or white portion of the bar at the top right corner of the screen to speed up the process.
If you only press the right bumper once, your character will reload his gun normally. Pressing RB while the pointer is on the grey portion of the bar reloads the weapon slightly faster. Press RB while the pointer is on the black portion and the bar will turn red, causing the weapon to jam.
You want to land the pointer on the small, white sliver for best results. This is referred to as a "Perfect Reload." Doing this will allow you to reload your weapon instantly. The gun also receives a slight damage boost for a short period of time. This added damage is where perfect reloads really shine.
Success is a matter of timing and practice. It may take awhile to get used to the Active Reload system, but don't fret, as you'll more than likely be pulling off Perfect Reloads fairly consistently in no time.