Arena and leagues
Arena is asynchronous PvP: you fight other players' saved builds, not the players themselves, and they fight yours while you are offline. Nothing about it is reflex-based, so an arena result is a straight verdict on the two builds, which makes it the most honest feedback the game gives you and occasionally the least comfortable.
How it works
You get 10 free battles a day and can buy more. Each one resolves from stats, gear, pet, potions and class effects on both sides, and moves your rating up or down. Rating sorts you into leagues, and because the ladder rewards accumulated rating rather than any single result, a good week of small wins beats one upset against somebody far above you.
Best practice
Read a loss as a matchup before reading it as a power gap. Armor penetration against a heavily armored opponent, healing reduction against a sustain build, and a defensive pet against a burst build all swing fights that raw stat totals say you should lose. The arena is where the pet elements stop being flavour and start being counters.
The common mistake
Chasing rating with the same build that clears dungeons. PvE opponents are stat blocks that fight straightforwardly; players bring specific answers. A build with no reply to healing or no way through armor can farm perfectly well and still stall in the arena, and the fix is a counter rather than more power.