Gas bubbles that form in a liquid, including the vapour bubbles that form as water boils, require tiny flaws (lack of homogeneity) to seed them. A baby bubble then adds other pockets of gas and grows, and once it has expanded to a certain size, it tears off and starts to rise.
In case of champagne the necessary flaws are found on the surface of the glass that contains it. Carbon dioxide bubbles form at preferred spots and rise up in a line from it. Those that originate at the bottom of a champagne glass are obvious because they rise to the middle. Others may form at the sides and slide up unnoticed because of the steep shape of the glass.
The bubble inception process is called nucleation, and the formation of the tiny pressure depression that lets it happen is called cavitation.
Surface tension (a tension of the surface film of a liquid, tending to minimise its surface area) on the surface of the bubble for-ms a barrier to bubble growth. It is very ha-rd to cavitate a pure fluid because it needs a little void to start the bubble. In other words, it takes a bubble to make a bubble.
To boil a liquid without an explosive effusion of it, chemists use a rough-surfaced object, a boiling stone, to encourage cavitation.
Sources: The Telegraph (Kolkata, India)