The words in the original is pranayam, lit., love. Nilakantha, however, explains it as meaning modesty, humility. I think, Nilakantha is right. The relations between Arjuna and the princess were like those between father and daughter.
“Uttara said, ’O Vrihannala, be thou a singer or a dancer, hold thou (for the present), without loss of time, the reins of my excellent steeds, mounting upon my car!’”
Vaisampayana continued, “Although that oppressor of foes, the son of Pandu, was acquainted with everything, yet in the presence of Uttara, he began to make many mistakes for the sake of fun. And when he sought to put the coat of mail on his body by raising it upwards, the large-eyed maidens, beholding it, burst out into a loud laughter. And seeing him quite ignorant of putting on armour, Uttara himself equipped Vrihannala with a costly coat of mail. And casing his own person in an excellent armour of solar effulgence, and hoisting his standard bearing the figure of a lion, the prince caused Vrihannala to become his charioteer. And with Vrihannala to hold his reins, the hero set out, taking with him many costly bows and a large number of beautiful arrows. And his friend, Uttara and her maidens then said unto Vrihannala, ’Do thou, O Vrihannala, bring for our dolls (when thou comest back) various kinds of good and fine cloths after vanquishing the Kurus assembled for battle of whom Bhishma and Drona are foremost!’ Thus addressed, Partha the son of Pandu, in a voice deep as the roar of the clouds, smilingly said unto that bevy of fair maidens. ’If thus Uttara can vanquish those mighty warriors in battle, I will certainly bring excellent and beautiful cloths.’”