Diablo 3's third season ran earlier this year, and now we're onto season four. For those who don't know what a season is, it's basically an excuse for you to start over with a new character, a "Seasonal Hero" that can only play with other Seasonal Heroes until the season is over.
These seasons feature new challenges and rewards, which in this case Blizzard says will include "new Legendaries, an exclusive Transmogrification set only available to those who compete in each Season, and Season-only achievements called Conquests." At the end of the season, your currency, materials, recipes, etc. will be transferred over to your non-seasonal profile.
There's also a new "Seasons Journey" interface that lets you track what's going on. Looks like this Season Journey gets you a new pet and portrait frame.
If you want to play season 4, create a new character and then make sure to check the "Seasonal Hero" box in the bottom-left corner of the character creation screen. Like this: