Pokemon events events are limited-time specials that allow you to get a certain Pokemon or item. Generally events are generally distributed through the use of Mystery Gift; sometimes they involve going to a game store like GameStop in real life and receiving it from Wi-Fi or sometimes they can be accessed from a home internet connection.
To get to the Mystery Gift menu, hit the "Mystery Gift" button on the menu where you usually press the button to continue your game. Hit the button that applies to you; generally Mystery Gifts are received through local wireless, so that is the option you will use (this won't work if your 3DS is not connected to the internet). If there is an event going on, you will receive it (this process takes time, be patient). You can claim your gift from the delivery man in the Pokemon Center when you next play the game.
More info on Bulbapedia and Serebii (this contains a guide which will help you access the Mystery Gift menu)