In just four short lines, the speaker describes a small moment that still feels big: two people look at each other, and one of them wants to smile. The poem is quiet about who the other person is, so the moment could belong to a stranger, a friend, or someone the speaker cares about more deeply.
What matters is what happens next. The speaker looks for some sign that a smile would be welcome, and there isn't one. "No answer was on sight," the poem says, so the smile is swallowed and kept "inside." The title, "No Smile," confirms that nothing was shown on the outside.
The mood is gentle but a little sad. There's no anger here, only the awkward disappointment of offering warmth and not seeing it returned, or not daring to offer it at all. The plain, simple wording makes the feeling easy to recognize: most people have held back a friendly gesture because they weren't sure it would be met.