It's a Big World, After All
You'll encounter a huge variety of objects as you adventure through Path of Exile. There are too many to reasonably cover in one section, so I've split them up roughly into the things you'll encounter in the early-, mid-, and late game.
On this page, we'll cover Waypoints, Town NPCs and Strongboxes.
Most zones in Path of Exile, although not all of them, have a Waypoint. Waypoints allow you to reach that zone immediately if you want to go back to a zone you've already been to, and it's usually a good idea to try to find the Waypoint in the zones you pass through. Clicking a Waypoint brings up your Map, and you can click any zone in which you've found the Waypoint to teleport there.
Path of Exile is set in a hostile world, but not so hostile that you'll never get any help. NPCs in town can offer you quests (most of which you will want to do) or act as vendors that will buy and sell items. Most NPCs also have story-related dialog that fleshes out the world and plot of Path of Exile, although you can skip this if you're not interested in following the story.
At least one NPC in each town also sells Skill Gems based on the class you're playing and the quests you've completed. In Act 1's town, the NPC in question is Nessa, who you'll meet as soon as you enter town for the first time. (In later acts, the easy way to remember the gem NPC is that it's always the female vendor in each town - Nessa in Act 1, Yeena in Act 2, Clarissa in Act 3, and Petarus and Vanja in Act 4.)
Boxes filled with loot! Everyone likes those, right? When clicked on, a Strongbox will spawn a few packs of monsters around it. Once you've killed all the monsters it spawns, the box will open and drop its loot on the ground.
Most Strongboxes are common and do not contain loot of any particular value. However, a few types found in the end-game - particularly the Diviner's and Cartographer's Strongboxes - can be very valuable.
Strongboxes, like items, can have different rarities: Normal (white), Magic (blue), Rare (yellow), or even Unique (orange). You can use Currency items on them to "craft" their mods just as you can with items. Some of these mods increase their loot drops, other mods make them more dangerous - watch out for boxes that explode corpses or Freeze you when activated!
For now, I would recommend that you do not use currency on them, except for using a Scroll of Wisdom to Identify their Affixes.