A second floor flat in the UK means two levels up from street level. That is, you have the ground floor flat at street level, then above that you have the first floor and then the second floor flat. In other countries, including the US, the terminology is different and the street level flat is called the first floor flat.
The UK 2nd floor flat has advantages for those that don't mind stairs and lifts. You are protected from some of the noise at street level, you are usually at less risk from burglaries, you have more privacy than floor beneath it and you also have better views and sometimes a balcony or roof terrace which again is more private than those on the 1st floor below. However, a 2nd floor flat is often not suitable for the elderly or those unfit to climb stairs if there is no lift. Unlike a ground floor flat your outdoor space is often a bit limited.
If the block of flats only has three stories then your 2nd floor flat is also the "penthouse" and has additional advantages of there being no noise above it and no through traffic on the lift or stairwell outside.