It means that the box is a singular, solid unit, and that it cannot be split across lines like an inline box can when its text cannot all fit on a single line. See section 9.4.2 which describes this splitting behavior and the terms "inline formatting context" and "line box".
If there is no longer any space on a line to fit an atomic inline box, the entire box wraps to the next line if there is a line break opportunity (otherwise it overflows the line box), even if the atomic inline box contains inline content that would partially fit the remaining space on the current line. This is because the inline content of an atomic inline doesn't participate in the same inline formatting context as the atomic inline itself — it participates in a separate inline formatting context within the atomic inline box, and therefore must remain within the boundaries of the atomic inline box.
Compare:
p {
width: 5em;
background-color: #f0f0f0;
}
span {
background-color: #d0d0d0;
}
.inline-block {
display: inline-block;
width: 4.5em;
}
<p>text <span class=inline>inline text</span> more text
<p>text <span class=inline-block>inline block</span> more text
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