How could they be moving faster than the speed of light?

Imagine two RC cars driving in opposite directions on a crumpled up, (virtually) infinitely large blanket with an uncountable number of ripples. The cars' top speeds are 10 MPH. On top of each car is an ant watching the other car.

Both cars start driving off at 10 MPH in opposite directions. From an ant's perspective on top of one car, the other car looks to be going 20 MPH away from it. Then someone starts pulling the blanket underneath the cars from opposite ends at 5 MPH. Now it looks like the other car is going 30 MPH. Now imagine for each ripple on that blanket, another hand appears and starts to pull, and the outer edges are pulled at 5MPH from the reference point of the nearest ripple.

From the perspective of an ant on one end, it can eventually get to the point that the other car is warping off at 100MPH or more. And as this blanket spreads out more and more, things speed up more and more as well. The cars never technically exceed their speed limits of 10 MPH, but the space that they occupy is being pulled apart in a way that they seem to be exceeding 10 MPH from each other's perspectives.

Anything which moves through space-time is restricted to moving at the speed of light. Space-time itself can warp causing objects to "move" away from each other faster than the speed of light.

Think of ants crawling on the surface and a balloon which is being blown up.

Because while matter cannot move faster than the speed of light the universe itself is allowed to expand faster than the speed of light. Think of the spacetime fabric stretching so fast light cannot cover the increased distance. The universe is essentially creating more distance between objects.

Another way to think of it is velocity of an object is derivative of position in space over time. If space itself is moving your position relative to it isn't changing.

I still can't intuitively understand this. If two objects ar stationary relative to each other, the expansion implies that at some point, the distance between those two objects will increase (without either of those objects having moved).

So space is being somehow created?! What if i have a large object, will the length of that object increase? Or will it break up?

The object is bound together by electromagnetic forces, and the local group is bound together by gravity. These forces are much stronger than the expansion of the universe (cosmological constant), but the expansion of the universe manifests as a tiny tiny outward pressure term (too small for us to detect). It makes every atom/orbit a little bigger by changing the equilibrium point, but they don't to grow in size because the force isn't increasing.

If the cosmological constant were much larger than it is, atoms would have never formed at all.

I think you are using a concept of space-time that is quite limited. You are at most using concepts from Einstein's Special Relativity. Everything changed with General Relativity.

Space is not "created", space-time is warped. Gravity is the deformation of space-time by mass/energy. The distance from point A to point B is measured by the time it takes for a light ray to get from A to B using the shortest path. But if you move objects with mass (or with energy) near A and B, the shortest path will change. Also, it's easy to measure distance in seconds when you know the speed of light.

If I understand this correctly, you're talking about something similar to Star Trek's Warp Drive (or the Alcubierre drive, for something less fictional). Instead of stars and galaxies moving at the speed of light, the space around them expands and the expansion accelerates at a rate that will eventually make the speed of expansion larger than the speed of light. Or in other words, stars and galaxies will continue to move at their sub-luminar speed, but the space in which they exist will expand so fast that the expansion will cause the distance between them to increase at such a rate that light will not be able to keep up.

[Edit: and, er, all that has something to do with dark energy?]

OK, but in that case, and if we still exist as a technological civilisation at that time (very doubtful) we might be able to use the effect for our own benefit. By building warp drives and er, not-quite-travelling faster than light, by expanding space around a ship, etc.

Warp drive solves a plot problem, it doesn't do anything to mitigate violating causality.

And if they can, why can’t we and catch them? I mean we are in spacetime. If it stretches we stretch too!

Right now the only serious effort to consider how to do so is the Alcubierre metric and its variations. Nobody knows how to build one, or what matrials could build one, or how to turn it on or off. Unless you have a cunning way to cheat, such as making the inside bigger than the outside, it requires in excess of minus the rest mass of the observable universe for a plausible sized object. There are further objections, but above my level.

So would the light from those stars also be moving outward faster than the speed of light?

No. In fact, if two objects are far enough apart, then the amount of new space created between them will be so great that light will never be able to travel between them. Neither object will ever be able to see the other.

It's really hard for me to imagine how a flashlight on a distance plant could be moving away from me faster than the speed of light but the emitted light is going slower.

No. It's color shifted though.

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

Just like the sound of an ambulance.