Unruh demonstrated theoretically that the notion of vacuum depends on the path of the observer through spacetime. From the viewpoint of the accelerating observer, the vacuum of the inertial observer will look like a state containing many particles in thermal equilibrium—a warm gas.
The Unruh effect would only appear to an accelerating observer. And although the Unruh effect would initially be perceived as counter-intuitive, it makes sense if the word vacuum is interpreted in the following specific way. In quantum field theory, the concept of "vacuum" is not the same as "empty space": Space is filled with the quantized fields that make up the universe. Vacuum is simply the lowest possible energy state of these fields.
The energy states of any quantized field are defined by the Hamiltonian, based on local conditions, including the time coordinate. According to special relativity, two observers moving relative to each other must use different time coordinates. If those observers are accelerating, there may be no shared coordinate system. Hence, the observers will see different quantum states and thus different vacua.
In some cases, the vacuum of one observer is not even in the space of quantum states of the other. In technical terms, this comes about because the two vacua lead to unitarily inequivalent representations of the quantum field canonical commutation relations. This is because two mutually accelerating observers may not be able to find a globally defined coordinate transformation relating their coordinate choices.
An accelerating observer will perceive an apparent event horizon forming (see Rindler spacetime). The existence of Unruh radiation could be linked to this apparent event horizon, putting it in the same conceptual framework as Hawking radiation. On the other hand, the theory of the Unruh effect explains that the definition of what constitutes a "particle" depends on the state of motion of the observer.
The free field needs to be decomposed into positive and negative frequency components before defining the creation and annihilation operators. This can only be done in spacetimes with a timelike Killing vector field. This decomposition happens to be different in Cartesian and Rindler coordinates (although the two are related by a Bogoliubov transformation). This explains why the "particle numbers", which are defined in terms of the creation and annihilation operators, are different in both coordinates.
The Rindler spacetime has a horizon, and locally any non-extremal black hole horizon is Rindler. So the Rindler spacetime gives the local properties of black holes and cosmological horizons. It is possible to rearrange the metric restricted to these regions to obtain the Rindler metric. The Unruh effect would then be the near-horizon form of Hawking radiation.
The Unruh effect is also expected to be present in de Sitter space.
It is worth stressing that the Unruh effect only says that, according to uniformly-accelerated observers, the vacuum state is a thermal state specified by its temperature, and one should resist reading too much into the thermal state or bath.  Different thermal states or baths at the same temperature need not be equal, for they depend on the Hamiltonian describing the system.  In particular, the thermal bath seen by accelerated observers in the vacuum state of a quantum field is not the same as a thermal state of the same field at the same temperature according to inertial observers.  Furthermore, uniformly accelerated observers, static with respect to each other, can have different proper accelerations  (depending on their separation), which is a direct consequence of relativistic red-shift effects.  This makes the Unruh temperature spatially inhomogeneous across the uniformly accelerated frame.