Inextricably is an adverb that means in a manner that is impossible to unravel or separate from something else. It is usually modifies words like "linked" and "tied." To most Americans, pilgrims and Thanksgiving are inextricably linked.
Inextricably is the adverb form of the adjective inextricable, which comes from the Latin word inextricabilis, meaning cannot be disentangled. In your mind, summer and the beach are inextricably tied together because you've spent your vacation at the shore for as long as you can remember. Circumstances might inextricably link you and your neighbor when you're trapped in an elevator together for the longest nine hours of your life.