What does the “~” (tilde/squiggle/twiddle) CSS selector mean?

The ~ selector is in fact the General sibling combinator (renamed to Subsequent-sibling combinator in selectors Level 4):

The general sibling combinator is made of the “tilde” (U+007E, ~) character that separates two sequences of simple selectors. The elements represented by the two sequences share the same parent in the document tree and the element represented by the first sequence precedes (not necessarily immediately) the element represented by the second one.

Consider the following example:

.a ~ .b {
  background-color: powderblue;
}

<ul>
  <li class="b">1st</li>
  <li class="a">2nd</li>
  <li>3rd</li>
  <li class="b">4th</li>
  <li class="b">5th</li>
</ul>

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.a ~ .b matches the 4th and 5th list item because they:

• Are .b elements
• Are siblings of .a
• Appear after .a in HTML source order.

Likewise, .check:checked ~ .content matches all .content elements that are siblings of .check:checked and appear after it.