Drop rate allows you to farm bosses, mobs, gear and items more efficiently. Many bosses have high drop rates of 1/10000 by progressing through the game and acquiring upgrades you can achieve over 1000% drop rate boost!
This means, if a boss has a drop of 1/10,000, if you have 1000% drop rate (10x your base of 1) this means we are hunting a 1/1,000 drop instead of 1/10,000 – THIS SAVES US SO MUCH TIME
Drop rate is not the only important factor though, DPS is key as well. see DPS
And that is how it works a bit complicated to explain but a far better system for overall balance
Also see Double Drop Rate