The quote that is attributed to him, "Come quickly, I am tasting the stars!" is supposedly what he said when tasting the first sparkling Champagne. Sadly, while the Dom did work tirelessly and successfully to improve the quality and renown of the still wines of Champagne, he did not invent sparkling wine, nor was the first to make Champagne.
In his era the refermentation in bottle that gives sparkling wine its sparkle was an enormous problem for winemakers. When the weather cooled off in the fall, fermentation would sometimes stop before all the fermentable sugars had been converted to alcohol. If the wine was bottled in this state, it became a literal time bomb. When the weather warmed in the spring, dormant yeast roused themselves and began generating carbon dioxide that would at best push the cork out of the bottle, and at worst explode, starting a chain reaction. Nearby bottles, also under pressure, would break from the shock of the first breakage, and so on, which was a hazard to employees and to that year's production. Dom Perignon thus tried to avoid refermentation. He did introduce some features that are hallmarks of Champagne today, particularly extensive blending from multiple vineyards.