In live sound the critical distance refers to the point at which sound reflecting from around the room begins to overpower the direct sound from the FOH speakers. This is shown in the diagram below.
At this point you would add another set of 'delay speakers' to re-enforce the sound to this part of the venue. Because the direct sound from the FOH can still be heard at a low level the audience will hear the sound from the 'delay speakers' and then milliseconds later the sound from the FOH speakers. To get rid of this delay you work out how long it takes for sound to travel from the FOH speakers to your critical distance. Then applying a delay to the 'Delay Speakers' will mean they produce could just as the sound from the FOH reaches the critical distance.
This technique is mostly used is larger venues but could also be used in smaller venues that aren't purpose built for music.
Info on critical distance from http://education.lenardaudio.com/en/04_acoustics_2.html
https://www.astralsound.com/speaker-position.htm
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