New to ARPGs?
ARPGs in a Nutshell
ARPGs ("action role-playing games") are the broader genre to which Path of Exile belongs. Despite the name, actual story role-playing is usually a minor part of them at most, and "RPG" here refers more to the notion that you're building a character that progresses through the game. Aside from Path of Exile, popular ARPGs include the Diablo, Fable, and Torchlight series.
ARPGs are built around the loot loop: kill stuff, get items, get stronger, kill bigger stuff for better items. The rest of the game is about figuring out how to kill harder things, figuring out how to kill weaker things more efficiently, gear crafting and trading to enable you to kill more and bigger things, and optimizing your build so as to kill things more smoothly. The fun of the game is in that loot, or in the reward it gives for optimizing your build properly - some players (like myself!) enjoy the planning as much or more than the play!
Path of Exile as an ARPG
PoE is no exception to the general rules above. While it has a story, it's optional and ignored by most long-time players, and will probably only be of interest to you the first time you play.
Typically, a session of PoE will be about clearing many areas of the monsters in them. Those monsters drop loot, which you can either equip for yourself, use as a base for crafting, break down into crafting currencies, or trade to other players. The stronger your character, the more and better loot you get.
You can also spend time out of combat crafting, with one of PoE's many currency items. Each currency allows you to modify an item in different ways: some allow you to change the modifiers (like extra life or resistances) it grants, others allow you to modify the sockets into which your character's skills fit. Basic crafting is pretty simple, but the depth of PoE's mechanics can sometimes allow advanced high-cost crafting to produce items of extreme power. As a newbie, you probably won't do much of this, but as you learn the game you might find it enjoyable to try to build the most powerful items available.