That depends on where you're from. In America, the first floor is the ground floor, so second floor is correct. In Britain, the first floor is the floor above the ground floor.
Edit: That was backward. Corrected now.
When you have a target of motion (going to somewhere, setting or hanging an object on something, etc.) it takes accusative case and not prepostional.
It is accusative; however, since it's inanimate and ends in a normal masculine ending (with a consonant as opposed to with an -а/-я) then it doesn't change endings.
Why it is in English the second floor and not the first? Do the English people count the floors now just like Russian people?
In English (British) the term ground floor is also used, describing the floor at ground level. Americans call it the first floor.
But we don't live in the ground floor. There are utility rooms, stores, salons of beauty, gyms in buildings and houses in the ground floor. Also there are ground floors in Malls.
In Russia there are ground floor (the minus first floor) , the first, the second...the eighty fourth and etc.
The same reason as why it's "I'm on the second floor" and not "in the second floor" in English, I guess.
To say 'we are walking on the second floor' would you use a different case for 'второй этаж'?
@Munky353786 - Yes, because then "second floor" is no longer a target of motion but rather a location. So you would use the prepositional case (Мы идем на втором этаже).
Though in that case it might sound more correct to use ходить rather than идти.