Milk clarification is a cocktail technique in which an acidic ingredient is used to curdle milk, separating it into curds and whey. The curd clumps act as filters that trap particulates, so that when a cloudy liquid is poured through them (such as a cocktail with lime juice that curdled the milk) it comes out clear. The curds stay behind and the whey goes into the clarified cocktail. 

This technique is used to make Milk Punch (aka Clarified Milk Punch or British Milk Punch). However beyond making tasty drinks, the clarification process acts as a preservative - the cocktail can now be stored at cellar temperature for months or longer - and also if shaken in a cocktail shaker it tends to make drinks frothy (though I think not for long). 

The clarification and the froth-production in the technique make it useful in many different ways, as have come to light when I've been interviewing bartenders for CocktailGreen. Here are some of the ways the technique is useful: 

Preservation of Whole Cocktails and of Just the Citrus

• You can use previous-day citrus juice in a milk punch cocktail rather than fresh juice, as the clarification strips the pulp bits leaving longer-lasting clear juice.
• Patrick Braga at Paper Plane in San Jose makes a "milk shrub" to get the whey from the milk plus the acetic acid from the vinegar and uses this in place of citrus in cocktails. 
• Similarly, according to this story in Liquor.com, Luis Hernandez of consulting company Cocktail Illustrators used "the lacto-fermented liquid from pickled carrots to use in a milk punch to act as the acid" (but still had to add additional acids). 
• I don't know of anyone who just clarifies citrus juice alone with this method, resulting in a citrus-whey mix. (If you're doing this at the bar, please let me know, we'd love examples.)

Batch Process

• Making milk punch makes sense for a batch of cocktails, and then the cocktails are (typically) ready-to-drink for quick service. You can do huge quantities at one time with big enough equipment. 
• If you have unused batch of cocktails after an event at the end of the night that would normally need to be discarded as it contains fresh citrus/other ingredients that will go off, you can milk clarify the batch to preserve it instead.  

Foamy Delights

• Dave Arnold's book Liquid Intelligence notes that you can "milk wash" base spirits like gin so that when they're mixed into cocktails they produce a nice foamy texture without using eggs. 
• Using aging citrus and citrus zests (rather than alcohol or a whole cocktail), Julian de Féral makes a sour mix foamer.

Use the Curds Too

• The leftovers from making milk punch are curds, but some bartenders have found ways to reuse those too:
  • Blend it into a cheese and serve as a cheese plate, make it into a dip, a grilled "cheese," or dehydrate it, according to Aisling Gammill of Water Bear Bar 
  • A Rum-peach-honey Milk Punch with a Panna Cotta recipe for the leftover curds from Allison Kave