What does the “>” (greater-than sign) CSS selector mean?

For example:

div > p.some_class {
  /* Some declarations */
}

What exactly does the > sign mean?

> is the child combinator, sometimes mistakenly called the direct descendant combinator.¹

That means the selector div > p.some_class only matches paragraphs of .some_class that are nested directly inside a div, and not any paragraphs that are nested further within. This implies that every element matching div > p.some_class necessarily also matches div p.some_class, with the descendant combinator (space), so the two are understandably often confused.

An illustration comparing the child combinator with the descendant combinator:

div > p.some_class { 
    background: yellow;
}

div p.some_class { 
    color: red;
}

<div>
    <p class="some_class">Some text here</p>     <!-- [1] div > p.some_class, div p.some_class -->
    <blockquote>
        <p class="some_class">More text here</p> <!-- [2] div p.some_class -->
    </blockquote>
</div>

Which elements are matched by which selectors?

1. Matched by both div > p.some_class and div p.some_class
   This p.some_class is located directly inside the div, hence a parent-child relationship is established between both elements. Since “child” is a type of “descendant”, any child element is by definition also a descendant. Therefore, both rules are applied.

2. Matched by only div p.some_class
   This p.some_class is contained by a blockquote within the div, rather than the div itself. Although this p.some_class is a descendant of the div, it’s not a child; it’s a grandchild. Therefore, only the rule with the descendant combinator in its selector is applied.

¹ _{Many people go further to call it “direct child” or “immediate child”, but that’s completely unnecessary (and incredibly annoying to me), because a child element is immediate by definition anyway, so they mean the exact same thing. There’s no such thing as an “indirect child”.}