To refute something means you maintain that something is not true or prove that something is wrong or incorrect. This is a verb you will hear used more often formal or academic contexts. You could refute a claim, refute an allegation or refute a theory.

1. The player released a statement to refute the claim that he was planning to retire at the end of the season. He said he was planning to play for another few years yet. 
2. The concept of global warming has yet to be convincingly refuted by skeptics within the scientific community. As such, they remain on the fringes of the debate on how the problem should be tackled.

1. The first thing we need to do after these shocking allegations is to refute them publicly in the press.
2. The figures you are quoting are outrageous. I have to refute them, my estimates are much more accurate.