Arena resets every Saturday.
Arena participation is important because we can obtain Arena chest rewarded after winning a challenge against other players.
The Advanced magic splinter, 10 of it will unlock your hero's Extended Skill slot. You could see this when you view your hero using the Hero menu (top left of the screen) The other splinter is used to research the extended skill.
Yep, the more reason to battle in the Arena.
And also, you can complete the Daily quest - Be victorious 1 time in the Arena.