What is the meaning of ‘profundity’?

Before dealing with the meaning, let’s deal with the pronunciation. The ‘o’ and the ‘i’ are like the ‘a’ in ‘china’. The second syllable sounds like the word ‘fund’, and the final ‘y’ is like the ‘i’ in ‘it’, ‘pit’, and ‘sit’. The word is pronounced ‘pre-FUN-de-ti’ with the stress on the second syllable.

When you talk about the profundity of a statement, you are implying that the meaning of the statement runs deep; the person who has made the remark has a clear and deep understanding the problem.