It was a trigger to condition the false memory. It's true he remembered Sammy, but every time he looked at the tattoo, he wasn't remembering the real story.
Sammy was actually a fraud, but the story that Leonard's tattoo was conditioning him to believe was that Sammy was telling the truth and that he killed his wife, when in reality that was Leonard's own life story.
According to his research while investigating Sammy Jenkins' claim was that amnesia patients should be able to learn new behaviors based upon instinct vs memory; that nesting can be conditioned versus remembered. The electrically charged figure test tried that tendency on Sammy and he failed the test which costed him his claim. Leonard's "remember Sammy Jenkins" tattoo did that for him so he could successfully deceive himself and alter his true past.