Dynamics processor for speech - apply gain on delayed samples?
It sounds better this way. 

Let's say you have limiter and you can't exceed a certain amplitude value (risk of clipping, for example). Now there is an audio event (say a snare hit) that peaks at twice that amplitude. If you just reduce this sample by sample instantaneously you create a lot of audible distortion. If you have look ahead, you can ramp down the gain smoothly so that by the time the audio even arrives, the gain is low enough so that you are not clipping any more.

Rapid gain changes tend to create a lot of audible artifacts. The look ahead buffer allows you to slow down the gain changes without the risk of creating an instantaneous out of bounds condition.  

It's also useful to look at a bit in the future when determining the gain for the current sample: if that's the highest point in the waveform can slow down the gain reduction, but if it's part of a slope, you probably want to maintain or increase your gain reduction speed.

Of course, you are not actually "looking into the future". Look ahead simply means that you put a delay on the processing path but NOT on the detection path of the dynamic processor.