What makes Citrate or Citric Acid an acid?
It depends on the pH of the solution.  At higher pHs the carboxyl groups will be dissociated (as drawn).  At lower pHs the equilibrium will shift and most of the COO- will become protonated.

In general, carboxylic acids are relatively weak compared to stronger acids that dissociate almost completely when added to an aqueous solution.  For example, acetic acid, or vinegar, will not burn a hole in cotton clothing, whereas sulfuric acid (the kind in an automobile battery) will easily burn a hole in cotton cloth.

Also, don’t confuse carboxylic acids with their carboxylate salts.  Sodium citrate, where the three protons are replaced with Na+, will act as a base when added to water, and raise the pH.