Something pertinent is relevant and on-point. If you give your best friend pertinent advice, that means the advice is appropriate for the situation.
Something pertinent is related to the current topic or situation — and probably helpful too. If you're in math class and you make a comment about World War I, that's likely not pertinent. If you're in music class and you talk about a cello, that probably is pertinent. Pertinent things are appropriate and logical. In most situations, people like to get comments and questions that are pertinent — anything else can just seem like a distraction.