We don't have to dig around too much to figure out what the title, "Silence," means. In the poem's lines 11-12, the speaker's father dishes out this bit of wisdom: "The deepest feeling always shows itself in silence;/ not in silence, but restraint." We've all heard versions of this before. Polonius, in William Shakespeare's Hamlet, warns his son Laertes, "Give thy thoughts no tongue…Give every man thy ear, but few thy voice," but our own parents probably used the less poetic "Mind your mouth!" or "Think before you speak!" to get the same point across.
We could say that "Silence" reveals two different reasons for why keeping quiet is often the best option. The speaker's father gives us the first reason directly. Talk is cheap; if we really care about something, we won't go running our mouths about it. Then again, however, we have to consider why silence, or restraint, is given so much value in a poem. Isn't writing a poem basically a way to talk (and sometimes talk a lot) about our deepest feelings?
Yes, we definitely shouldn't miss the title's irony. It claims the poem is about silence, but then 14 lines of verse follow it. And almost all those lines are quoted from the man who says silence is so important. This gets at the second reason we might want to think before we speak. If we say something, just as the father does, who knows what our listener will do with what we said? Our listener could always repeat our words – even turn our words into a (maybe ironic) poem! Anything we say immediately becomes public property, and that's the implied warning "Silence" gives us.