Much less than, what does that mean?

The entire point is that it's NOT very clear what "much less than" is. What is "much less than"? In some contexts $1\ll 2$ and in others $ 1\not \ll 2$ but $1 \ll 100000$ and in others, even $1\not\ll 100000$. What precisely makes something "much less than"?

In most contexts, $\ll$ is used in approximation. For example: for $0<x\ll 1$, $(1+x)^n\approx 1+nx$.

So how small does $x$ have to be? Well small enough for the approximation to be "good enough"! What is good enough? It seems like I'm just pushing off the question, and that's indeed what I'm doing!

The entire point isn't whether something is "small enough" (big enough), or if the approximation is "good enough", the point is control. Can you control the error in a manageable way.

For the example $0<x \ll 1, (1+x)^n \approx 1+nx$. You can make $(1+x)^n$ as close as you'd like to $1+nx$ by making $x$ small enough! I think this is a more rigorous meaning.

$\ll$ is imprecise in the sense that you don't know how "small" something is. But it is precise in the sense that it implies that there is some control. There is some way of making the error in the approximation, argument, etc. as small as you'd like, provided that you make $x$ small enough.

"Much less than" is a qualitative assessment of comparative inequality.

$a\ll b$ means that $a$ is not only less than $b$, but muchly so by some convention.

That convention is fairly arbitrary, or rather contextual; there is no fixed quantitative basis.   Sometimes it is based on additive position, sometimes on multiplicative magnitude.   It's mostly based on utility and context; it's a declaration that $a$ is less enough than $b$ to be useful in the discussion (such as the case where certain terms involving $a$ become vanishingly small enough to conveniently ignore).   To know what sufficiently less means, you have to understand what the context of the comparison is.

In certain contexts (primarily in Number Theory), $a(x) \ll b(x)$ is an alternative notation to $a(x) = O(b(x))$. See e.g. this question.