They Unlock when your level gets to I think 26 or so. So you need to be on the look out for any rare or Legendary armor to increase your light level. Or get some of the Vendor gear. Vanguard stuff takes Vanguard marks. Gained by doing Patrols(will go slow) Or Strikes or the Daily Story Missions.(I think they give marks too. I might be wrong) Crucible Gear takes Crucible Marks Gained by doing the PVP playlists ect. Then you have Faction Gear. you need Crucible Marks for them as well. Or, you equip a factions Class Item as you play Strikes or strike playlists, Do patrol and turn in bounty's. After Rank 3 (vanguard/Crucible/Faction) they send you a thank you package that sometimes can have armor. (This will take a long time. as any armor or items in the package is all up to RNG) Also Exotic Armor can help with this as well.

Once you get better armour, there is a stat that comes with it called 'light'. Inspect anyones characters gear and you would see that Discipline, Strength, and/or Intellect is paired with Light. The higher the light value, the higher the level would be. Inspect me if you will.

the nightfall is level 32 and the weekly 32,30,26 you have to be within three light level to unlock them 23 for the 26 27 for the 30 29 for the 32

You need to unlock gear that has light which will then boost up your light level you unlock them at lvl 30ish

You need to be at least lvl 23 for weekly and 29 for nightfall.