In Parshat Chayei Sarah (כד:יז) it says וירץ העבד לקראתה ויאמר הגמיאיני נא מעט מים מכדך. The literal sense is that Eliezer wanted to see if the woman would give him water to drink as well as for the camels. But in addition, he wanted to see if she possessed both good qualities and wisdom. Eliezer wanted to see what Rivkah would do with the water left over in the pitcher after he had drunk. On one hand, she could not take it home to her family because it was unsanitary. But if she threw it out, it would be an insult to Eliezer. That is why it was important that she say וגם לגמליך אשקה, "I'll give your camels water as well." By offering water to the camels she not only avoided insulting אליעזר, she also made it look like she was not even trying to avoid insulting Eliezer, and thus she did not embarrass Eliezer.