In meditation, labeling is a technique wherein you recognize when your attention has wandered from your focus of meditation (e.g. breath, body etc.).  You notice a thought that comes in, let it go and return to your point of focus. The underlying principle is that identifying  the thought, and distinguishing it from your current experience, makes you thus less likely to be overwhelmed or carried away by the thought, leading to a calmer mind and body.

In negotiation, labeling is calling out an emotion you perceived in your counterpart in sympathetic fashion to get them to better explain themselves or help you better understand their perspective. Similarly,  the underlying concept here is that identifying and distinguishing the emotion from the ongoing negotiation gives you better chances for a successful outcome.

In  emotional psychology, labeling is identifying when an emotion arises in your mind and body, and giving a name to it (e.g. fear, tiredness, anxiety). This helps you recognize the emotion as separate from your being, hence you can dissociate it from your person in order to handle as what it is - an emotion, not you, it’s watcher - and regulate it accordingly. The more accurately and the more the granularity with which you can label the various emotions engulfing you at a given moment, the better you can handle them. And labeling grants you a measure of self-compassion in dealing with the emotions.

These 3  domains demonstrate the importance of establishing a separation between emotions and their host as a gateway to handling them effectively. 

Here’s an analogy on improper labeling or not labeling at all and some possible effects. 

Think of your car. A strange noise starts to emanate from the rear. Unless you have other reasons to doubt the integrity of the specific vehicle, it is unlikely that you would conclude that it is entirely a bad car. Chances are greater that you resolve that the noise is due to a faulty component of the car. The more skilled you are at identifying the affected module (and sub modules) based on the unwelcome noise, the faster you can isolate and fix it. 

It would surely be ill-advised to drive your car around in that state especially if you did not resolve or at least identify the issue for several reasons among which are: 

1.    One corrupt module not addressed could propagate its negative effects out so that the next module too is affected or damaged. 

2.    Knowing that something is wrong (though you cannot properly identify it), you may avoid a given situation which the car would actually rather handle pretty well as its defect does not impact its performance in that situation. Or you might, overlooking the defect, get into a situation that the car will not handle well, precisely as a result of its defect. 

Labelling is identifying as a first step that a defect is present, and distinguishing the defect from the car - knowing that a component is faulty, not the car. And then, even when you are not necessarily able to resolve it instantly, driving with knowledge of the defected component, probable cause and ensuing limitations of the car.

There is enormous benefit in being able to identify the various thoughts and emotions emerging in day to day situations we face and breaking them down to better see the various individual factors and components involved. This in turn grants us clarity, so we do not throw the baby out with the bath water.