Bubbles are carbon dioxide dissoved in the water, and is called carbonic acid. It enhances flavours, especially other acids like orange, lime, lemon or tamarind. Bubbles make otherwise mediocre cocktails sparkle with taste. E.g. try adding a dash of club soda to a Vodka + orange juice, and you will be amazed at the difference.
And when bubbles are released from water, they add a fizzy mouthfeel, which elevates the cocktail to a new level.
The best way to get bubbles is to use alocohol which already has bubbles in it. This is the case with champagne, prosecco, cava etc.
The simplest way to add bubbles to a cocktail is by adding club soda or tonic water or Coke. Some bartenders dont want to dilute the base ingredients with soda, so they carbonate the ingredients themselves, e.g. fruite juices with a machine like Soda Stream.
Also, Foam.