The character conceit of The Secret World is that you are a normal person who suddenly gains "powers" and is then recruited and trained by one of three secret societies: the Illuminati, the Templars, and the Dragon.
Character creation is reasonably good, you have a fair amount of options when it comes to your face and starting outfit. I created a female, Coriel, and joined the Templar faction. The Illuminati are far and away the most popular society, and I don't know anything about the Dragon other than there is a bit of oral sex in the Dragon introduction.
The Secret World does not have classes or explicit levels. However, it does have roles and implicit levels. It is a fair bit different from most MMOs, and does take a little getting used to.
What abilities you get depends on your weapon, and your training with the weapon. Weapons are central to characters. The idea is that you channel your powers through your weapon. There are 3 weapon categories: guns, magic, and melee weapons. There are 3 weapons in each category: pistols, shotguns, rifles, chaos magic, blood magic, elemental magic, swords, hammers, and claws.
The basic idea is that you must have a rifle equipped to use a rifle ability. As you earn experience points you gain Ability Points that you can spend to unlock passive and active abilities in each weapon. Costs tend to follow a pattern where the first few abilities are very cheap, and then the cost steadily rises. However, the most expensive abilities appear to be more specialized, rather than strictly better damage.
The key element here is that you are only allowed 7 active abilities and 7 passive abilities at any one time. But you can wield two weapons. So you spend Ability Points to gain abilities with the two weapons you have chosen, and mix and match abilities to create a useful set of 7.
Actual combat is very similar to other MMOs. You target creatures and use abilities. The general pattern is combo point generators and finishers. However, there are some subtleties. Guns generate combo points on the target. Magic generates combo points on the character. Melee also generates points on the character, but I think the points are automatically gained with time (when in combat), without necessarily needing to use generators.
Certain weapons adhere to certain roles. Healing can be found in rifles, blood magic, and claws. Tanking is swords, hammers, and chaos magic. Most other trees have support abilities in addition to damage. As well, different weapons prefer or create different conditions, so it's up to you to use two weapons which synergize.
The thing is that Ability Points do not increase character power directly, they only give you more abilities. Character progression is governed by gear. Gear has "Quality Levels", and you are more powerful with better gear. But you can't just wear any gear.
In addition to Ability Points, there are Skill Points. Skill Points are earned 1 every 3 Ability Points. You invest Skill Points into each weapon and gear type. Each level of skill costs increasing points, but also gives you a bonus with that weapon. You can't equip weapons or gear which are more than one level higher than your skill. So this is the aspect which creates the implicit levels.
Monsters and missions essentially take your current gear into account when determining if something is easy or hard. You'll see people asking for groups by QL. For example, people like QL3 for the first dungeon (which I didn't get to).
So basically, there is a short steep vertical progression, but also a fairly broad horizontal progression. There are twelve or so default builds given in the game, so you can just follow those builds if you are at a loss. I think you even get some cosmetic outfits if you complete a default build.
Gear is essentially amulets and trinkets, in addition to your weapons. Clothing is separate and cosmetic, and I guess must be bought or given as mission rewards.
The thing about The Secret World is that missions are repeatable if you want, they have a cooldown of a day or so after you finish them. So you are never stuck without a way to earn XP. There's no such thing as "respeccing" because you just earn more AP and SP. In theory, one could eventually unlock every single weapon ability and every single skill level.
For example, I figured Coriel would play as a healer, so I chose my first weapon as a rifle. After a while I put a couple of points into pistols for my second weapon. But I didn't like pistols, so I went to elemental magic instead. I have one elemental attack, and one elemental passive that puts a small DoT on the mob when I crit, even with a rifle attack.
Gear is role dependent. Tank gear has more health and less attack power. Healing gear has +heal instead of +attack, which does not boost your damage abilities. This may cause some people to shy away from healing and tanking roles. But it's not a permanent choice.
However, The Secret World also has my favorite UI element: a defensive and offensive target, as in Warhammer Online. Thus a lot of the healing abilities, especially with rifles, are really "leeches" which convert damage to healing.
I think that's a reasonable overview of character progression. The key points are weapons being the focus through which everything flows and determining playstyle, Ability Points to unlock usable abilities, a restricted set of passive and active abilities that can be used at any given time, and Skill Points to govern the quality of gear that your character can use.
1. I was looking on the forums, and some of the theorycrafters were talking about a concept called "bridge passives" which are passive abilities from a third weapon tree that could be used to get two non-synergistic weapons to play nicely with each other.