Something that's distinguishable can be detected or observed, especially as being separate or different from something else. The one chocolate sea salt doughnut in the box will be easily distinguishable from the plain doughnuts.
In some people with color blindness, red isn't distinguishable from green — in other words, it can't be perceived as a different, separate color. You might complain that the policies of your city's new mayor, despite her promises, are barely distinguishable from those of her predecessor. The verb distinguish is at the heart of this adjective, and it comes from the Latin distinguere, "to separate between."