The Passive Tree
The core of Path of Exile's character customization is its massive Passive Skill Tree of well over a thousand nodes. It looks like this (but don't panic!):
(Note: because the passive tree changes with different patches, your exact tree in-game may look somewhat different from the one above - but it's the same basic structure. You can find an updated, interactive version of the current passive tree on the official Path of Exile website here.)
Each node on the passive tree grants some effect to your character. For example, many nodes that benefit spells are found near the top of the tree, and many nodes that benefit melee weapons are found near the bottom left. In general, each "wheel" or "cluster" on the tree is themed around one particular sort of benefit: for example, the cluster at the bottom center focuses on bonuses to characters using shields.
Connecting these wheels are "roads" made of nodes that simply grant one of PoE's main three Attributes: Intelligence, Dexterity, or Strength. These attributes determine what weapons your character can equip, what skills they can use, and what kind of armor they can wear - see "Classes & Attributes" for more on the details.
Since your character can't specialize in everything, much of the tree won't be of interest to any particular build (which is why it's not as complicated as it looks). Instead, you'll travel to the areas of the tree that do interest your build, picking up secondary effects (particularly increases to your Life, in most builds) along the way.
As your character levels up, and as they complete certain quests as part of PoE's main story line, you'll gain Passive Skill Points. Each point allows you to unlock one node on the passive tree, similarly to (say) a Diablo skill tree or most MMORPGs' talent trees.
All in all, you'll get just over 100 passive points to spend in your build, depending on exactly what level you reach. The maximum possible, as of this writing, is 123, for a Level 100 character who made certain decisions during the main storyline. In practice if you're reading this guide you're not likely to hit Level 100 anytime soon - it requires enormous time investment and precise play. So you'll have somewhat fewer than that. Builds included with this guide, for example, are based around 103 or 101 points (depending on the details of their story choices).
Depending on what class you chose (we'll talk about classes in a later section), you'll begin at different points on the tree. However, all seven classes share the same overall passive tree, so it is possible for any class to access any passive node in principle. In practice, you will often - although not always - want to pick a class that starts near nodes that benefit your build.
Notables & Keystones
Each "wheel" or "cluster" on the tree contains at least one Notable Passive. These have larger icons on the tree and tend to provide better bonuses than the smaller nodes around them, but are otherwise fairly similar. They also have special names, which make it easier to figure out which area of the tree someone is talking about.
Keystones, on the other hand, are another story. Keystone passives are the largest nodes on the tree, and provide some major change to the way your character works, sometimes breaking the normal rules of the game in the process. Almost all keystones have both a positive and a negative effect, so they are not things you generally want to include in just any build.
For example, the Avatar of Fire keystone passive converts half of your non-fire damage into fire damage (which means you can specialize in scaling fire damage exclusively). However, it also prevents you from dealing any non-fire damage in any way, meaning that you don't want to take it in just any build. Similarly, the Point Blank keystone makes your projectile attacks do far more damage to targets close to you, but much less to those far away. As a result, it's strong for builds that get up close and personal and terrible for those that don't.