The rough surface contains a large number of small bubbles, trapped in the crevices of the glass. These bubbles grow with the addition of carbon dioxide from the beer, until they become too large. The free portion splits off and rises, while the trapped part begins the growth-split process all over again. The rough surface provides more locations for these bubble generators. The rough surface should also resist deactivation through frequent washing.
Surface tension increases the pressure inside a bubble inversely as the radius decreases, so the formation of new bubble is highly unlikely. http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html
Some times, you can see the effect of some small impurity in the beer. A stream of bubbles will rise from a point that floats around in the beer.
As an aside, physicist David Glaser https://en.wikipedia.org/wiki/Donald_A._Glaser developed his Nobel prize winning bubble chamber using (among other liquids) beer as the fluid medium. He has denied that beer bubbles were his inspiration, but...
The beer inside a bottle has carbon dioxide inside it.
When the top is opened the pressure above the beer is reduced and the beer becomes supersaturated with carbon dioxide. There is too much carbon dioxide in solution.
To reduce the amount of carbon dioxide in the beer the carbon dioxide which is in solution has to become a vapour. This requires a number of molecules to come together to form a vapour and at the same time create a surface between the vapour and liquid phase. This requires energy.
The formation of vapour bubbles is a complex process but it is helped by the vapour bubbles forming on nucleation centres. In the case of beer in a glass these may be imperfections (edges, points, crevices) in the walls of the glass which are now added by some glass manufacturers during glass production and any small particute matter in the beer.