There is a massive, thrice repeated discretely instances battlefield(s) known as World vs. World. It pits 3 servers against each other weekly. Servers are ranked and move up & down the standings. The battlefield is one based around supply depots and control points.
Alternatively, there are smaller CP based battlefields which are akin to the instanced battleground/warfronts seen in other MMOs such as Tera, The Secret World or World of Warcraft.
There are PVP-ish mini games too. Such as costume brawl, a dodge-ball like game and one similar to hide-n-go seek. For example.
Should read the wiki first for all GW2 questions. It's a fairly good overview of all functioning systems of play.
The cool thing about structured PvP is you don't need to level up or grind gear. It's instant 80 with your choice of stats, runes, sigils, weapons, abilities, etc. Want to play a necromancer? Instant. A Engineer? Go for it