Use the adverb arguably to describe something that can be asserted or shown to be a certain way. For example, you might say that your favorite teacher is arguably the best teacher in your school.
If you declare that a certain restaurant makes what's arguably the best milkshake in town, you mean that a solid argument can be made in favor of their shakes. Use arguably when you want to emphasize or back up a statement or opinion. The word was first used in the late 19th century to mean "as may be shown by argument," from the Latin root word arguere, "make known, prove, or demonstrate."