"I tried to get my work done on time." If taken literally, we could expect two possible results from this. 1. I succeeded in getting my work done on time. 2. I failed to get my work done on time.
However, most people will understand that I meant the second result. Saying that I tried to do something implies that I tried and failed. If I had succeeded, I would just say, "I got my work done on time."
The author is saying that there is more to conversation than the literal meaning of sentences. There is implied information, contextual clues, etc.
This is why A is correct. To understand that I was trying to say that I failed to get my work done, one would need an understanding beyond the literal definition of my words.
