Answer:
Primary fermentation is when wort becomes beer through the conversion of sugars into alcohol and carbon dioxide. This conversion is facilitated by adding yeast which "eat" the sugars. Generally takes 7-14 days, but the only way to be sure that fermentation is complete is to measure the Gravity.
"Secondary fermentation" is somewhat of a misnomer as fermentation really is finished at this stage. Secondary fermentation is more used to clear and condition the beer. As beer is transferred from the primary to the secondary a lot of the sediment is filtered out. This allows the beer to age nicely. Dry hopping can also be completed at this stage. I'm of the opinion that this step is not terribly necessary, unless you will be dry hopping or are wanting a really clean, crisp, clear, light, etc. beer.
Rule of Thumb: 1, 2, 3
That is 1 week in the primary, 2 weeks in secondary, 3 weeks bottle conditioning. Of course this timeframe does vary depending on the type of beer you are brewing.