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rel·e·vance

  [rel-uh-vuhns] Show IPA

noun the condition of being relevant, or connected with the matter at hand: Some traditional institutions of the media lack relevance in this digital age.

Relevance is a derivitive of the word "relevant".   Relevant means how much something matters or is pertinent to something else. 
Example:  On TV, you sometimes hear an attorney object and say, "Irrelevant, Your Honor". That means the attorney feels that what the other attorney is asking about doesn't make a hill  of beans difference in the case.  (Kinda like it's B.S.)

Some synonyms (words that mean the same or nearly the same) for relevant include:
having a close and logical relationship
pertinent, or immediate and direct bearing in the matter
applicable, meaning that it has bearing on the matter at hand
apropos, appropriate

Antonyms (opposite of ) include:  inappropriate, extraneous (outside of), immaterial, irrelevant