Space isn't empty. The view of quantum mechanics is that space is filled with things called 'fields' - basically the potential for particles to exist. The phrases 'electromagnetic field' and 'gravitational field' are widely used.
Electromagnetic fields can be easily messed about with by us - they are the basis of all electric motors, for example, and you can feel the forces of attraction and repulsion by playing with fridge magnets. The gravitational field is very much weaker, and we can't easily control it, for several reasons - the first is that the gravitational force per particle of matter or unit of energy is extremely small and so the force is only significant from large amounts of matter. We can't build a hand-held source of gravitation in the same was as we can build a hand-held source of electromagnetism (a torch). The second reason is that gravity is almost always positive - there is no convenient anti-gravity source we can use to cancel it out.
So, we have some experience of fields, but there are many more fields that we can't easily interact with without vast and expensive machines like particle colliders. There are at least fields for each kind of particle. There are electron fields for example. When particles collide in colliders they shake at these fields and, depending on the energy of the collision, they may be able to produce a wave in the field, and that wave is a particle. Shaking up the fields that fill the vacuum is the way that particles can be made, but it's not the only way. Quantum mechanics is based on the observation that there is always uncertainty (although very precisely defined amounts). There is uncertainty in the rippling of the quantum fields. That uncertainty allows for waves (particles) to spontaneously appear and disappear. These temporary waves are called 'virtual particles'.
Considering just waves in the electromagnetic field, these virtual particles - in this case particles of light - will appear at a range of wavelengths, from gamma rays to radio waves. Empty space is filled with these fluctuations in quantum fields.
However, we know how to block ripples in the electromagnetic field - metal cannot be penetrated by either radio waves or light. So, if you were in space and you had a metal box with you, such as a cake tin, and you closed the lid, what would be in the box? There would be all the ripples and fluctuations of the quantum fields in the vacuum - except for the ones that could not fit! There is no way that a radio wave of metres in length could fit into a cake tin! So, that cake tin would be in a strange state - it would be emptier than space!