Video productions monitor using screens. Audio productions monitor using loudspeakers that are driven by amplifiers.
Every decision made in a musical production (not only regarding sounds but also arrangements and even performances) is based on what everyone is hearing.
For example, if you’re recording a bass sound and the monitors sound thin, you may mistakenly believe that the bass sound itself is thin and compensate by adding more bottom. Then when you hear the same sound in a different location you may find that the sound has too much bottom and is muddy.
Likewise, if a singer is performing and cannot hear the proper blend of music and their voice, they will not be able to perform as comfortably and to their fullest potential.
As stated above, every decision made in a musical production will be based on what people hear. What people hear can be affected by many things, including loudspeaker type and condition, amplifier type and condition, headphone type and condition, quality of wire and soldering, ear wax, sinus congestion due to colds or allergies, ear fatigue, and the changing acoustics as people move around in the room. Even air pressure (based on weather and altitude) can affect how things sound.
Going back to the video comparison, you would not crank up the amount of “red” on the screen before you adjusted the color of the video itself. Video monitors can be set differently in a variety of ways, and screens display colors differently as they age. Colors on a screen can even look different if viewed in a dark rather than a well-lit room. And looking at the sun for a few seconds makes it difficult to properly see and judge any image (much like the ear fatigue from listening to very loud music makes it difficult to properly hear and judge any sound).
Similarly in audio, volume is very important. Human sensitivity to frequencies (our ability to hear bass, midrange and treble) is different depending on the volume of what we are listening to (thanks Fletcher & Munson). When we listen quietly, we hear frequencies less evenly. When we listen loudly, we fatigue our ears and the speakers.
Another variable that can change how you hear something is perspective (actually, perspective affects how you judge what you hear). Listening to material that has extra bass or treble will affect how you perceive and even judge the next thing you hear. If you listen to rap and reggae all day and then try to mix a punk rock song, you may judge that the kick and bass sounds need to have more bottom when they may actually be appropriate for the musical style.