If a permanent entering causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.
Permanents entering don't cause abilities of permanents your opponents control to trigger.
Elesh Norn doubles all your own enters-the-battlefield triggers while completely shutting off your opponents' ETB triggers, turning a blink/value engine into a soft-lock asymmetric advantage machine. You ramp into Norn, flicker your own creatures for doubled value, and grind opponents out of resources while their flicker, landfall, and ETB strategies sputter. Close games by snowballing token, lifegain, or stax payoffs into an overwhelming board.
Doubles every ETB and entering-related trigger you control, generating absurd value
Hard-shuts off opponents' ETB triggers, blink decks, and many landfall/token engines
Mono-white gives access to the best stax and taxes pieces
Cheap at 5 mana with vigilance, so she blocks and attacks
Single removal target; mono-white struggles to recover after she dies
No card draw or ramp built in—relies on the rest of the deck
Doesn't help against decks that win via combat, spells, or attack triggers
Color-screwed against fast combo with no interaction of her own