Think about an audio setup as a chain of elements. If an element has a "fault", e.g. some attenuation of a frequency range, you can of course correct this element if possible. If not, you may correct the fault by another element.
Examples:
- a vinyl has a rising frequency response due to the RIAA eq during the cutting. The cartidge as the next element does not correct this but the following element = phono preamp applies an inverse RIAA eq. Thus the correction is following the fault
- a speaker driver plays too loud due to its higher efficiency. The wise speaker designer corrects this fault by attenuating the voltage for the driver in the speaker crossover. This correction is preceding the faulty element.
You can characterize the transfer behaviour of each element as a filter. The end result is thus the convolution result of the filter elelments. For LTI systems (indeed we truly hope our system belongs to this class) the commutative law is also applicable for convolution. This means we can correct a fault by the element, by previous elements or by following elements.
Example: you can place some porous but absorbing material near to your ears and thus the high frequency range get dampened. If a mastering engineer knows about this he can prep the music track accordingly and you may love to listen to this track.
THIS DOES NOT CORRECT THE SITUATION OF THE ABSORBER, IT IS STILL THERE.
Like the simple examples a room behaves like a filter. The only trouble: it behaves like a very complex filter. Thus it is not possible to correct everything. But anyway the sound gets better despite the room does not change.
Again an example: the room has some reverberation time. In case of a resonance (standing wave) you need little energy to get a loud signal. Whereas other frequencies behave well you get a bass boost at this frequency with same input voltage. When you stop the signal the reverberation time is pretty long. It simply takes time to dissipate the energy. Now a room correction reduces the voltage, it applies an attenuation at htis frequency. This also means that there is much less energy in the room. As the sound level is lower it also takes less time until it is below the listening threshold. So you experience a shorter reverberation time DESPITE the room is not changed at all.
So typically with room correction you can notice a cleaner sound instead of muddiness.
Last but not least it is possible to measure again with applied room correction. Despite the unchanged room the measurement clearly proves the effect of the correction filter.
If you now like to place your ears directly close to the speaker you will of course notice a "weirdo" sound. But this is only because now you take off the element 'room' out of the playback chain