A test for an ion is unique if only that one ion gives the result. If two different ions gave the same result, a positive test would not tell you which ion was present, so you could not be certain of your answer.
Many tests need more than one step to make them unique. Sodium hydroxide gives a white precipitate with both aluminium ions and calcium ions, so that result alone is not enough. Adding excess sodium hydroxide separates them: the aluminium hydroxide precipitate dissolves, but the calcium hydroxide precipitate does not.
Acid is also used to remove ions that would interfere. Barium chloride gives a white precipitate with carbonate ions as well as sulfate ions, so dilute hydrochloric acid is added first to destroy the carbonate. In the same way, nitric acid is added before silver nitrate so that carbonate cannot give a false white precipitate when you are testing for chloride.
In an unknown salt, a chemist therefore uses several tests and combines the results, so that every ion is identified without doubt.