If it's your turn to talk in front of the whole class, and you're feeling shy or nervous, your friends might coax you. They might say, "You can do it! Get up there! You've got this!" With their smiles and their words, your friends can coax you into speaking clearly and confidently to the entire class.
Typically, we coax people into doing things that they kind of don't want to do, but we really want them to try. For example, you could coax your little sibling into trying a bite of a new vegetable. She doesn't want to, but you'd really like her to, so you use gentle words, and you're patient: you say, "Please? Just try a little bite?" That's what coaxing sounds like. It's gentle.
When Gru has no interest in reading the girls a bedtime story, Agnes coaxes him into it, saying "Pretty please?" Gru gives in to her coaxing. He reads them the story.