This command is to order the platoon to look towards the the Colors and Battalion Commander as they march past.
Along with the Battalion Commander, several dignitaries may also be present with him. These dignitaries may include heads of state, congressmen and even the President.
Since many people are disappointed with Obama, including the Armed Forces, this "inside joke" has a strong foundation. The "inside joke" is to command "Eyes Left!" so that the platoon looks away from Obama instead of towards him.
This offense is punishable in a military court, so the order will never be heard nor followed. But in secrecy, in the military bases, in the bars outside of the bases, and at the homes of fellow men, "Eyes Left" means that you are upset with the way Obama is running the country.
Military Man 2: Eyes Left!