The easiest and safest visualization of space increasing is to simply think of it in terms of geometry.
The distance or volume of space increases, Space itself is not a substance, energy or material, it has no properties other than distance or volume. The increase in volume/distance is simply filled with the energy-mass content of the universe already present.
A good treatment and one that is applicable, is to think of a fluid, or ideal gas. The metrics involved in Cosmology are essentially ideal gas treatments. As the volume of space increases the density of that ideal gas decreases as well as the temperature. Just like classic gases. Though you also have to consider quantum effects such as virtual particles and quantum tunneling, but that's a different subject
On my initial post I included a Universe Geometry article, look at the term critical density, Critical density is the calculated value that would have a flat and static (Non expanding/contracting) universe. The energy-density to pressure relation of each particle species is defined by the equations of state (Cosmology). The universe geometry is an energy-density, (corresponding pressure) relation between positive pressure (gravity/matter) and negative pressure (Cosmological constant). Expansion and the geometry (flat, curved) pressure distributions affects the path of light rays
So remember an increase in space is simply a geometric change in volume/distance that is simply filled with the contents of the universe. Space is neither created, destroyed, or stretched/compressed. Multimedia tends to use the simplest and often confusing terms due to time constraints and sales of their programming. You have to admit some of the terms used do get a lot of attention
here is the critical density portion from that article,
The topography of the universe is determined by a comparison of the actual density (total density) as compared to the critical density. The critical density is represented by the following formula
\rho_{crit} = \frac{3c^2H^2}{8\pi G}
\rho=energy/mass density
c=speed of light
G= gravitational constant.
density is represented by the Greek letter Omega \Omega so critical density is \Omega crit