In Chapter 3, Douglass explains an idiom that is common among enslaved people but that would not immediately make sense to his white Northern readers:
The slaveholders have been known to send in spies among their slaves, to ascertain their views and feelings in regard to their condition. The frequency of this has had the effect to establish among the slaves the maxim, that a still tongue makes a wise head. They suppress the truth rather than take the consequences of telling it, and in so doing prove themselves a part of the human family.
Douglass refers to the phrase, "a still tongue makes a wise head," as a maxim among enslaved people. This means that it is a commonly uttered piece of advice. Maxims are usually self-evident phrases, but this one is not self-evident to someone who has not lived through the experience Douglass describes. Because it requires context that many of Douglass's readers don't have until Douglass offers it, the phrase functions in the book as an idiom.
A "still tongue," or silence, is considered necessary for someone to have a "wise head" because, based on what Douglass and other enslaved people have seen, nothing good comes of speaking the truth about the way they are treated. Sometimes, an enslaved person who is honest about their experience might be forced to endure physical abuse. Other times, enslavers may break up their family by selling family members to other enslavers. Out of self-preservation, the idiom suggests, it is wise to keep silent about abuse on the plantation.
The idea that there are spies trying to entrap people into saying bad things about their enslavers emphasizes what an astonishing and necessary thing it is for Douglass to lay out the truth of his life as he is doing in his narrative. Enslaved people are coerced into silence even among each other about the abuses they endure. It's not that they don't want to speak up or that they think enslavement isn't worth speaking out against, it's that they must stay silent to survive. Otherwise, they may be "found out" as someone who is willing not to protect their enslaver's reputation.
Keeping silent and even lying about their experience is demoralizing and dehumanizing for Douglass and other enslaved people. Douglass is suggesting that telling the truth (allowing one's tongue not to be still) is a human right. He is standing up for this right by writing his narrative. This passage asks white readers, indirectly, to reflect on how it must feel not to be able to tell the truth of their own lives. It helps them understand that if they have not heard much testimony by enslaved people against the institution of slavery, it is not necessarily because they don't have complaints. Finally, the passage encourages readers to make it safer for enslaved people to tell their stories.