The Haas effect is one of those psychoacoustic effects that a lot of audio folks forget about or have often never heard of but it’s extremely useful to know about and can make a huge difference to how you mix. The Haas effect is closely related to the precedence effect (often also referred to as the law of the first wavefront). In short our ears/brain will always localize the first sound we hear, even if a reflection of that sounds comes from somewhere else we still perceive that sound has having come from the original first received sounds direction. A single reflection (>1ms delay, up to 10dB louder) will increase the perceived loudness and width without changing the localization and without making it sound as if it was a separate sound event and this even goes up from 5ms to 30ms. We still perceive that as one sound.
There are some factors that increase or decrease that time threshold where we start perceiving things as an echo instead of one sound but you can easily try this out for yourself with a panned reverb or delay plug-in. What you see is not what you hear in this case and it’s important to know about when mixing.
Most commonly this effect is exploited in large events / concerts where a single front of speakers wouldn’t be able to cover the whole audience at a suitable SPL. In such cases delay towers are set up that are calibrated to delay the sound by the time it takes the main stage speakers to reach the point of the delay tower (~340m/sec), then 10-20 ms of delay are added on top. Why those extra 10-20ms? That’s the part where the Haas effect is exploited to make sure that the audience still perceives the original sound as originating from the stage speakers but increase the SPL. Otherwise we would perceive the sound as originating from the delay towers which will make the audience feel disconnected from the performer on the stage. Another positive side effect of this is that the people standing right underneath or slightly in front of the delay towers (who will experience some leakage especially in the lows to mids as those frequencies are less directional) again won’t perceive the delay towers speakers as the originating sound source. You can imagine it would be quite disconcerting to watch a concert in front of you and have the music reach you from behind you!
For more reading check out Wikipedia’s article or the Handbook for Sound Engineers has a great overview section on psychoacoustical effects and then there’s of course the original papers. A quick web search should find you a ton of results.