It's not a mode, NIVVSACC666 - it's just called the "Adventure update" because it adds some things that make it more of a game. Things like a hunger bar, which slowly drops throughout the game - this means that food has more of a purpose now, since your hearts won't regenerate if you're starving.
It also adds XP that you can collect from killing enemies, which can then be used on an enchanting table to craft better weapons and tools that have special effects such as lasting longer or knocking enemies back when you hit them.