What does this "double less than or equals to" sign mean?

It means exactly the same as $\le$.

It is the same old $\le$ symbol.

Mathematical notation is far from set in stone or standardised, as might appear to a beginner. Here's a sample of the variations in the inequality signs (taken from symbols-a4.pdf):

Of course, most of this is not commonly used; my guess is that they have been included only for historical purposes and for completeness.

I add a comment for the sake of completeness. As said, in general $\geqq$ means $\geq$, but in some old math texts it is possible to find the following distinction for a real vector $x$:

• "Positive" denoted as $x > 0$: all the elements of $x$ are strictly positive;
• "Semipositive" denoted as $ x \geq 0$: all the elements of $x$ are nonnegative but at least one of them is strictly positive;
• "Nonnegative" denoted as $ x \geqq 0$: all the elements of $x$ are nonnegative.

In other terms, with this notation, $x \geq 0$ implies $x \neq 0$.