First of all, trivially in order to understand what it means for something to happen, we need to be able to distinguish what happens from what does not. It is the ability to distinguish these that provides meaning to both.
As to the significance of things that don't or didn't happen, there are several important kinds of example. Here are a few suggestions, not an exhaustive list.
In law, there is the concept of negligence. We consider that under some circumstances, a person may be held liable for something they failed to do but could and should have done.
More generally, in ethics, a similar principle applies. We may consider a person to have failed in their moral responsibility by not acting in accordance with moral principles or virtues.
In our understanding of causation, we typically appeal to the concept of what would have happened if, or if not. Correct judgments about causal relations are typically said to support a corresponding counterfactual conditional. If we are sure that what caused the plane to crash was a bird strike then counterfactually if the bird strike had not happened, the plane would not have crashed. Considerations of this kind are highly practical in avoiding future disasters, since they assist in planning and decision making.
Similar considerations apply to events that might have happened but didn't, but where the consequences of them happening would have been very serious. If the winter had lasted any longer, our food supplies would have run out. This provides a motivation for making better preparations for future winters. We can learn from events that nearly happened but didn't.
Historians like to speculate about what-if scenarios. What would have happened if Caesar had lost to Pompey? What would have happened if Churchill had agreed an armistice with Germany after the fall of France in 1940? Maybe there are lessons to be learned from considering such scenarios.
Sometimes when making inferences, we have to consider situations that we know to be false in order to eliminate some possibility. If the victim had been shot, we would expect to see an entrance wound for the bullet, but there is none, so we can eliminate shooting. More generally, reasoning by reductio involves hypothetical consideration of things that are not true. If X were the case, a contradiction or absurdity would follow, so X is false.
Sometimes scientific experiments can have negative results that are signficant. Perhaps the most important of these was the Michelson-Morley experiment, which attempted to measure the motion of the Earth relative to the lumeniferous aether and failed to find any.
There are other uses of counterfactuals in philosophy, e.g. Nozick's counterfactual theory of knowledge. I expect if I stopped to think about it, I could find several more.