The slightest means the smallest possible amount or degree of something. It's the superlative form of “slight,” used to emphasize just how tiny or minimal something is.

You'll often hear it in negative statements: She didn't show the slightest interest in the movie means she showed absolutely zero interest. He left without the slightest hesitation means he didn't pause for even a fraction of a second. The word adds emphasis, stressing that not even a trace of something exists.

The slightest sound can wake a light sleeper. The slightest breeze can knock over a house of cards. The slightest mistake in a recipe might ruin the whole dish. In each case, the word highlights how little it takes to matter: the tiniest bit, the most minimal amount, the absolute least amount.