Depending on the specific cutoff date you've got, I'd argue that smokeless gunpowder in 1886 is the single most important breakthrough. Smokeless powder paved the way for firearms as we know them today. Smokeless powder burns slightly differently than black powder (rapid burn rather than low explosive) and is significantly cleaner on firing. Although the immediate effect is apparent in the name - less smoke means it's easier to see on the battlefield - the more significant benefit was the significantly cleaner result of firing, meaning guns no longer had to be designed around regular cleaning after fewer than a hundred rounds. This in turn allowed bores and bullets to decrease in size (as the utility of large bores with respect to getting more shots between having to clean was gone) while velocities went up, allowing for flatter-shooting, longer-ranged weapons. Smokeless powder also proved far more conducive to autoloading systems thanks to higher pressures and cleaner burns, which made machineguns a truly viable weapon on the battlefield.

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Prior to that, percussion caps and brass drawing were very important steps. Percussion caps at first allowed for a quicker and more convenient way to prime a gun compared to a flint lock, but they ultimately provided the foundation for the primers in every modern cartridge. Meanwhile, brass drawing provided an effective and consistent means to contain cartridges that could be mass-produced. Unlike paper cartridges, they left no residue in the chamber after firing, and unlike rolled brass cartridges, they were sturdier and easier to produce.