The speaker has told someone how they feel, and the reply is nothing at all. No words, no laugh, no change in tone, not even a flicker of reaction. The poem builds around the repeated line "The silence is deafening," which works like a drumbeat. Each time it returns, the quiet feels heavier, and the speaker's hurt grows with it.
The title's pun on "sigh-lence" points to the one sound in the poem: the speaker's own deep sigh. Early on, the speaker mentions ear plugs, as if to block out noise, but the idea turns bitter by the end. The plugs are "of no aid" because this isn't ordinary noise. It is the pain of being ignored. The other person walks away "as if you were never there," and the speaker is left feeling invisible, as though their thoughts and feelings don't matter. The mood is awkward, lonely, and quietly crushing, and the final switch from "The" to "Your" silence turns it into a direct accusation.