The ~ selector is in fact the subsequent-sibling combinator (previously called general sibling combinator until 2017):

The subsequent-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>

.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.