How does the drone measure altitude? If I start with 55 meters and I fly to a hill that is 75 ft high will it be flying 55 meters high on the hill?

Your Phantom uses a barometer to measure altitude.
All altitudes are relative to where you launch.
Home = zero.

Like Labroides mentioned, the IMU module will provide the altitude info for the drone, and it is relative altitude.

The altitude is calibrated and set  from the point at which you start the engines.  It is measured AGL ( Above Ground level), not sea level.  In other words, if you live in a city that is located 2,000 feet above sea level and you start the engines, the altitude will show "0" feet. (more or less).  As you fly, the altitude shown will increase relative to that takeoff point, not the terrain you are flying over.