"an artist of the floating world" の主人公、OnoはMaster Takedaのところで働いていましたが、もっと優れた画家から声がかかり、同じくTakedaの所で働いているTortoise(あだ名)に君も推薦してあげると言った場面です。
'But Ono-san, what are you saying?' he said in a lowered voice. 'Master Takeda took me on through the recommendation of a most respected acquaintance of my father. And really, he has shown me great tolerance, despite all my problems. How can I be so disloyal as to leave after only a few month?' Then suddenly, the Tortoise seemed to see the import of his word, and added hurriedly: 'But of course, Ono-san, I don't imply you are in any way disloyal. Circumstances are different in your case. I wouldn't presume...'
"import of his word" の意味は文脈から、彼の言葉の意味・重要性と思えますが、"import" の意味としては輸入とか、コンピュータのソフトで使われるエクスポート(技術用語・送出の意味)位しか知りません。 "import" が "important" と関係があると話は早いのですが、どうでしょう? 辞書を見ます。
・Merriam-Webster's Online Dictionary: importance; especially : relative importance: it is hard to judge the import of this decision
・Cambridge Dictionaries Online: formal importance or meaning: Whether it is to be a 'working' visit or an 'official' visit is of little/no import.
・Dictionary.com: meaning; implication; purport: He felt the import of her words
なるほど、"import" は絶対的な意味・重要性ではなく相対的なものとのニュアンスに違いがあるものの "important" と関係があったのですね。