If an effect would create one or more tokens under your control, it creates twice that many of those tokens instead.
If an effect would put one or more counters on a permanent you control, it puts twice that many of those counters on that permanent instead.
The tokens and counters that Doubling Season creates are exact copies of the kind of tokens and counters that were being created in the first place.
Doubling Season affects cards that “enter the battlefield with” a certain number of counters. Triskelion, for example, would enter the battlefield with six +1/+1 counters on it rather than three.
If there are two Doubling Seasons on the battlefield, then the number of tokens or counters is four times the original number. If there are three on the battlefield, then the number of tokens or counters is eight times the original number, and so on.
Planeswalkers will enter the battlefield with double the normal amount of loyalty counters. However, if you activate an ability whose cost has you put loyalty counters on a planeswalker, the number you put on isn’t doubled. This is because those counters are put on as a cost, not as an effect.