Another "easy" way to say it:
If you know the climb gradient the aircraft will produce during each takeoff segment, it can then be compared to the terrain and obstacle heights in the takeoff path. Airport analysis requires both of these components to ensure the airplane can climb clear of terrain and obstacles.
The segments exist so that the airplane climb gradient can be enumerated for each configuration and speed schedule used (segment) during the climb to a safe altitude with the assumption of one engine having failed on the runway at Vef. OEI climb gradient tables or graphs are published for each segment for part 25 certificated airplanes in their respective AFM. This data is also most often digitized for computer software to crunch.
Lots of useful tutorial material on the inerwebs...
Familiarity with
this document (Skybrary) may be of assistance in preparation for a technical interview. The takeoff performance brief begins on page 49.