Can someone explain what Wittgenstein was trying to say in Tractatus Logico-Philosophicus ? Specifically propositions 6.341-6.343. What does he mean when he says that a system like Newtonian Mechanics does not assert something about the world but can describe it?
Wittgenstein is getting at the idea that any formal system rests on certain arbitrarily-chosen conventions, and by choosing different arbitrary conventions we can create different formal systems that represent exactly the same physical reality.
For instance, because of early history we habitually do plane geometry on a flat plane with orthogonal axes. Thus, if we want to measure the height of a building we use the (horizontal) distance to the building and the angle of a line to the top of the building to calculate the (orthogonally vertical) height. But as I'm sure you're aware, it's perfectly possible to construct a flat plane in polar coordinates rather than orthogonal axes. If we worked habitually in polar coordinates, most of our basic geometric formulae would have different structures, but it would still be a complete geometry, and still describe the world in a comparable way.
In the same sense, using decimal 12, binary 1100, hexadecimal C, or Roman XII is an indifferent, arbitrary choice of numeric base. They all point at the same 'thing' in the real world (two six-packs of your beverage of choice, say), so which you choose is a matter of convention or convenience.
The larger point Wittgenstein is reaching for, here, is that when we talk about the 'System of Newtonian Mechanics' or some such, we are talking about a particular set of conventions and rules that we use to model the real world, but that don't in and of themselves say anything about the real world except as they happen to capture the way the world is. In other words, the world does not behave according to Newton's Laws; the world does what it does, and Newton's laws are one way among (perhaps) many of capturing or describing what the world does.