The soft level capacity is at 20, yes. That means when you reach level 20, experience will no longer make you level any more. If you want to go past level 20, you'll need Motes of Light to buy equipment from the Speaker. This armor will have a stat called Light which determines how many more levels past 20 you can get to. Max level 32. This increases when new content is added to Destiny.
EDIT:
The class items bought from the Speaker does not give any stats. So the only way to get equipment with the Light stat is to kill enemies and hope for good equipment with the light stat. Only higher level equipment will have the light stat.
EDIT 2 (Feb 6, 2015)
Motes of Light are given to you when you accumulate experience after you've reached level 20. Equipment with the Light stat can be bought from the Vanguards and from Xûr. It can also be awarded after missions, strikes, raids, and battles in the Crucible/Iron Banner. The rarer the equipment, the more light.
UPDATE: (May 19, 2015)
With house of Wolves out now the new level cap is 34. You can use etheric light to ascend (upgrade) any of your old legendary or exotics though to catch up with the new gear and level cap. Get more info here: http://goo.gl/VPztvk
Update: (September 9, 2015)
With Update 2.0.0 the Character Level Cap will be increased to 40 on 9/15/15, and you no longer need armors' light stat to further increase your effective level. It's now purely EXP based. There is also now a gear score component, where each equippable gear piece's defense or a attack level contributes to your overall light level. This maxes out at 310, and is based on the average value (possibly with some weighting) of all of your currently equipped gear.
Update: (April 12, 2016)
Bungie released their Update 2.2.0 on April 12th, 2016. The Light Level was increased to 335; the maximum XP level still caps at 40
Update: (September 20th, 2016)
In the Rise of Iron Expansion, Bungie increased the maximum light to 385
The engram will decrypt into another exotic item, not the same item. However, you may get an item for the hunter. There is only a very small chance that it will be the same item that you received from decrypting the exotic engram you already bought.
Best Answer
The light "level" of your character is an average of your gear's light.
For this reason, at level 34 when everyone only had 170 gear the "cap" was 170. Now, for the same reason, the cap of gear's light level will be the cap of player light level.
I have seen prior that the new Trials of Osiris lighthouse gear will be given out fully maxed at 310. This leads me to believe that 310 is the cap for gear, and by relation 310 would be the light level cap.
As the release was only yesterday, there is obviously going to be more information to come, but for now this is as close as possible.
List of Taken King known gear
Video of several 310 Trials pieces along with other new gear
310 Auto Rifle Doctrine of Passing (Adept)destinyDB "Death is the best teacher"
edit
After playing for some more time, here is the breakdown.
Non raid gear, even blues and legendaries, will only drop with a cap of 300.
In order to reach this pre raid level, it is best to identify your items from the cryptarch one item at a time, ensuring to equip it as you go if it is a higher light level - this will affect future light levels in identified engrams.
In general, the raid is very smooth with a light level of 295.
So if you do not raid, your light level will cap at 300. In order to reach the 310 gear the raid must be completed or attempted. At which point, a full 310 set would place your guardian at 310 which is the overall cap.
Now with hardmode out dropping 320, and Trials gear dropping 320, the cap is at 320 light. Some surmise that it is not possible to reach without an Artifact however this is incorrect. As the light level of your character is an average, if you never get an artifact that slot is not included in the average. The result is that several people have taken advantage of this and reached 320 already. There is probably something to be said for a tradeoff of stats (lost int,disc,str) but it is possible and achieved at present.