"When 1-gram precision is high, the reference tends to satisfy adequacy.
When longer n-gram precision is high, the reference tends to account for fluency."
What does this mean?
Adequacy: How much of the source information is preserved?
Fluency: How good is the generated target language quality?
For Machine Translation task,
English(S-V-O): A dog chased a cat
Reference translation in Hindi would look like:
Hindi(S-O-V): A dog a cat chased
When 1-gram precision is high, correct word-to-word translations will be high but order of those words might not be correct in translated sentence. But still, majority of the source information is preserved.
High 1-gram, low N-gram(2-gram) precision value example: chased dog cat
When N-gram precision is high, order of those words will be preserved to some extent and you would get a fluent sentence in Hindi.
High N-gram(2-gram) precision example: A dog cat chased