When she finished giving him to drink, she said, "I will draw water for your camels, too, until they finish drinking."
The Torah could have written that he ended drinking, why did the Torah write that she ended giving him to drink?
The Ohr Hachaim explains that not only did she give him to drink, she held the cup to his mouth and was completely in charge of his drinking. He did not have to bother himself at all.
He then offers another pshat. The possuk says וְׁנָתַתִּי עֵשֶׂב בְׁשָדְׁ ךָ לִּבְׁהֶׂמְׁתֶׂךָ וְׁאָכַלְׁתָ וְׁשָבָעְׁתָ - I will give grass in your fields for your livestock, and you shall eat and be full. The Gemara deduces from this possuk that a person may not eat until he has fed his animals.
However, this only applies to a person who wishes to eat a regular meal. When a person is desperate, the Halacha changes. If he is in danger of passing out due to thirst, he may drink first.
When Eliezer asked for a little water, she realized that he was very thirsty and desperate, and she gave him to drink immediately. But, as soon as she had given him a little to drink, she assumed the danger was past. Now she stopped giving him to drink and turned to his camels, whose thirst takes precedence.
Indeed, when she gave them to drink, she gave them עַד אִּם כִּלּוּ לִּשְׁתֹּת – until they finished drinking. They were allowed to drink as much as they wanted, they weren’t limited by anything.
