Not sure if I am qualified to answer it, but this sentence seems to try to define what is science and the development or the structure of it---
The first step of the process begins with "careful observation" which is "perception of a pattern in the phenomena observed" because according to the structure of the sentence, "careful observation" = "perception of a pattern in the phenomena observed" (meaning observe in order to find the pattern of things)
Then the second step ('cause it says the first step is "followed by" this) in the process is "exploitation (meaning the full development) of this knowledge (knowledge referring to the pattern found by observation)"
These two steps of the process make up one area of the human activity we call "science."
Simply put, it's--> observation + exploitation = science