Nintendo events are events where Nintendo gives away certain Pokémon and tickets to get to rare or legendary Pokémon not usually found in-game.
Here is a list of the different tickets and items available from Nintendo Events:
Eon Ticket
Mystic Ticket
Aurora Ticket
Old Sea Chart
Here is a list of Pokémon available from Pokémon events:
Toys'R'us Give-away
Journey Across America