Here's a decent write-up:
Source
Since Destiny is not your typical FPS, it combines a bit of Borderlands looting and Diablo 3 progression and is nothing like Halo, I'm sure some of you might find it a bit confusing. So, i am going to break down what the "End Game" at level 20 is about, and hope this helps you plan ahead and get enjoyment out of what is inevitably a grind-fest.
Yes, you are going to have to grind.
Anyone familiar with Diablo 3 or MMOs in general are familiar with this concept. It will become tedious and annoying, but when you get your first piece of shiny Purple, it will all be worth it. If grinding is not your thing, then there is plenty of exploring to do i suppose.
First, figure out what you want to focus on AT FIRST: PvE or PvP. This is not a major issue in the bigger picture, you can obviously do both, however, to get your FIRST piece of Purple, it will help you tremendously to pick one or the either, and stick with that for a bit.
Why is this? Because there are three different vendors you can get gear from: Your Class Vendor/Vanguard Armory, The Crucible Vendor, or any of the Faction Vendors. Your Class Vendor/Vanguard Armory requires Vanguard Marks, and the rest require Crucible Marks. So, if you want to focus on PvE, then just stick with your Class Vendor for now. However, if you want to focus on PvP, then you should probably pick something from the Crucible Vendors at first.
Everyone requires Reputation before you can purchase Purple equipment from them. Your Class Vendor requires Vanguard Rank 2 for Armor pieces, and Rank 3 for Weapons. Crucible Vendor requires Crucible Rank 2 for Armor, Rank 3 Weapons. Factions requires Rank 2 with that Faction to purchase Armor, Rank 3 for Weapons.
How Do you get reputation?
Ah, now we are getting to the Grinding. Vanguard (PvE) rank is simple: you can do Strike Playlists, which will put you in a random Strike, and you will earn Rep AND Marks (Marks are the currency used to purchase equipment). On the Left side of your screen will be a "Daily Heroic Story" which will award bonus Vanguard Marks once a day for completing that specific Story mission Hard Mode. Below that is a Weekly Heroic Strike, which will also award rep and marks, but is limited to once a week. You can also do Vanguard bounties and Patrols for reputation. You are capped at 100 Marks a week though, but you can grind until you get Rep 3 all you wish.
For PvP, it is set up pretty much the same, except you just have to participate in the Crucible to get Marks and Reputation. You can also do Crucible specific Bounties to increase your Crucible Rep.
As you can see, this is why it helps to pick which mode you want to focus on at first, since you are going to have to grind rep with either Vanguard or Crucible to 2 and then 3, and then use the Marks to purchase gear.
Ah, but what about Factions?
Factions (Dead Orbit, Future War Cult, New Monarchy) are a bit trickier since they require their own Rep, AND Crucible Marks to purchase items. If you wish to go that route, simply purchase one of their Class Armor items when you hit 20 (should be the only thing you can actually purchase), equip it, and start earning Rep by the same way you earn rep listed above, but now it will count towards that Faction, instead of Vanguard or Crucible rep.
What's the level cap?
Well, technically there isn't one. Once you hit 20, you stop gaining levels from Experience points. Instead, your post-20 levels (21, 22, etc) are based on your GEAR. Specifically, a new stat listed on higher level gear (usually Blues) thats called "Light." When you equip a piece of equipment with the Light stat on it, it is like adding a small bit of XP to your progress bar to 21. Equip enough pieces with Light, and you will hit 21. You must seek out better gear with even higher Light stat numbers on them to level to 22, then 23, etc. Its a long process to say the least. Also, dont forget to upgrade your gear, because it will also increase the Light stat number on that piece of gear, getting you ever closer to the next level.
Edit...picture explaining Light Level:
http://imgur.com/aUN5QFP
As you can see, i have "28" points in Light, and the Bar is about 75% full, so im guessing i need 40 Points I need 32 points of Light to hit 22, so i need gear with an additional 4 points of light combined to hit level 22.
This game is designed for the End-game grind (like most MMOs are). You will want to upgrade your gear so you can do harder missions, which in turn will drop better gear, and more marks and reps to allow you to buy the bestest gear. Or, you can just play nothing but Crucible, grind rep, do Crucible bounties, get your Marks and purchase them that way. In either case, it is a grind. So good luck!!