Rafiq Jan, in Qatar, asked about the meaning of the phrase "intellectually fertile."
To understand the meaning of a phrase, it's often helpful to look at the meanings of the individual words.
Combining these two words
When these two words are combined, in the phrase intellectually fertile, they mean “producing a large amount of serious thought," or, put more naturally, "producing many serious ideas.”
Here is an example sentence with this phrase:
In this sentence, the writer is saying that informal conversation in college dining halls can sometimes produce more serious ideas than class discussions.
I hope this helps.