Secret of Arcana is a new power provided by the Dragonborn DLC. You acquire the power by completing the black book "Filament and Filigree", found in Kolbjorn Barrow after defeating the dreaded Ahzidal.
The description of the power understates the great power it gives you. "Spells cost no Magicka for 30 seconds." All of your spells will have 0 cost for 30 seconds, that much is obvious. The lesser known benefit is how Secret of Arcana also affects enchantments!
Secret of Arcana will allow you to use weapons with low charges for 30 seconds. This makes Keening a viable weapon. Keening only has 1 charge which makes it useless. Other great weapons like Harkon's Sword need to be recharged over and over. Now thanks to Secret of Arcana you can use these weapons without having to refill them after 10 hits.
Master spell casting is where Secret of Arcana really shines brightest. You do not need enchantments or perks to cast high powered spells. Just turn on Secret of Arcana and unleash your fury!
Thrall spells are my favorite to use with Secret of Arcana. They are usually impossible to cast without a ton of spellcost reducing perks and enchantments. Because thralls hangs around until they are killed you do not cast the spells often. Secret of Arcana is perfect since you do not need to cast thrall spells more than once a day. A great Dead Thrall will stay with you a lot longer, so why waste perks and enchantments when you rarely use the spell they are intended for?
Staves are also affected by Secret of Arcana. You can use the power to cast the staff spell for 30 seconds without the need to refill the staff. This allows your characters to be a pretty powerful mage without learning the spells, spending perks on the magic skill or putting points into magicka.
Some people will say 30 seconds, once per day, is not a big deal. Well those people are wrong! Being able to cast unlimited spells for 30 seconds will get you through the toughest situation in any dungeon, especially a difficul boss fight. Imagine casting blizzard for 5 or 6 consecutive times! If there is an enemy still standing after Secret of Arcana times out you should probably run and never come back!
An unintended benefit (glitch) of Secret of Arcana is how concentration spells will continue costing nothing after the power times out as long as you continue holding down the spell button. You can use this to level certain Alteration very quickly. Do this with Detect Life or Telekinesis and you can get to level 100 very easily.
The spell tome for Telekinesis can be found at any level in Redwater Den (with Dawnguard) or Benkongerike (Dragonborn). Using Secret of Arcana with Telekinesis will get you to level 100 in one swoop, fast traveling from Riften to Markarth.