An eye dropper was a tool used to collect and distribute liquids.
In 2372, Tom Paris recalled feeding a baby bird with an eye dropper, which inspired him to use a hypospray to feed the reptohumanoid he and Neelix encountered on Planet Hell. (VOY: "Parturition")
In 2374, Jadzia Dax mused to Quark that the decision to put liquid latinum inside solid gold was probably made by someone who got tired of making change with an eye dropper. (DS9: "Who Mourns for Morn?")