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.
Doubling Season is one of the format's premier "build-around payoff" enchantments, and its split nature lets it shine in two very different shells.
For token decks (Rhys, Adeline, Krenko, go-wide aristocrats), every creature/Treasure/Clue generator doubles—turning a single trigger into board-warping value. For +1/+1 counter decks (Atraxa, Ghave, Hardened Scales builds), it doubles every counter, snowballing your creatures absurdly fast.
The real reason it commands a premium is superfriends: it doubles loyalty counters, meaning your planeswalkers enter with double loyalty and can often ultimate the turn they land. That's a game-defining swing.
When NOT to play it: it does nothing the turn you cast it—it's a do-nothing five-mana enchantment unless you immediately follow up. It's also a "win-more" magnet that paints a target on you. Skip it in decks without a critical mass of token or counter sources; in those, it's just an overpriced vanilla enchantment that gets blown up before it pays off.