'Equilibrium' is basically the point at which the gasses in the column have settled into roughly separated layers based upon their density and boiling point.

When the liquid in the boiler first begins to boil, large quantities of gas beign to rise up the column. If the column is very short, the state of the gases in the column is initially very turbulent, with very poor separation of components. Given enough time and the condition that none of these gases escape, they will eventually settle into fairly well-defined layers.

The best example of this I can give in common, visual terms is an imiscible solution or suspension of very fine particles. Italian dressing is a good example. If a bottle containing oil, vinegar and herbs is shaken, the result is what can basically be called a mixture. Despite the fact that the components do not really form a true solution, their repulsion to each other is fairly weak, and a rough approximation of a mixture of the two can be created. Given enough time undisturbed, however, the liquids in the bottle will eventually form fairly discrete layers again. This is basically what happens in the column. The initial boiling is like shaking the bottle. Refluxing is like leaving it alone to settle. The difference is that, in the case of hot gases which will naturally rise and attempt to leave the system, these must be 'caught' or condensed into liquid and returned to the system.

If all of these gasses are condensed and returned to the column, the still is said to be operating in 'full reflux mode'. Eventually, given fairly constant heat input, they will form these layers inside the column. The addition of structured packing ,such as copper scrubbers or ceramic raschig rings, serves to accellerate this process by providing a greater surface area for these hot gasses to pass through, thereby forcing them to condense and re-evaporate all throughout the column. By using a longer column, this accellerates the process even further because the space the gasses must pass through is greater. Generally, given a sufficient column length, the column can be said to be at equilibrium once the gasses reach the top.

Maintaining this, however, is another matter. See the post I made here.