What is Leona's Secret Passive?

Solution 1:

Sunlight: Leona's passive Sunlight deals one less damage to champion skins wearing sunglasses (eg. Surfer Singed and the Commando skins).

Source: http://leagueoflegends.wikia.com/wiki/Hidden_passive

Here is a link to the LOL files, where the information of the wiki comes.

Another source, is a video of Rift Myths:

NOTE: There is a bug in Jarvan's Commando skin and he do not receive less damage.

As of this writing, so far, there've been only theories/rumors about Leona's passive. I'm also waiting for a confirmation.

Phreak did give a hint:

Some Demacian champions are affected.

Some claims include, but are not limited to the ff. (I'm still waiting for confirmation for any of them):

Unconfirmed but close: She deals 1 less damage against Demacian champions with Commando skins (sunglasses). See this thread.
Confirmed but debunked: Her W breaking Banshee's shield even before it explodes, and revealing herself to enemy units even when she's in bushes or within the fog of war (see screenshots here and here). This can be explained by looking further into the mechanics of the spell.

Here are other theories, but most of them are unconfirmed:

Slightly increased Sight Range(Her or Allies) Dance can cause damage
Miss Chance when facing her
Her Shield of Daybreak(Q) might give a small sight into a nearby bush
She gets miniscule buffs/debuffs depending on what map is used, e.g. Summoner's Rift Summer/Autumn
She gains a miniscule buff when laning with Pantheon

Of course, there's the slight possibility that we've been trolled.