What is meant by the "affectionate" woman whom the Messenger (peace be upon him) urged us to marry, and how can a woman be so without that leading to her husband neglecting her, especially if he is divorced?

The Hadith you are asking about is: "Marry the affectionate (al-wadud), the prolific (al-walud), for I shall outnumber the other nations by you." It was narrated by Abu Dawud and authenticated by Al-Albani. Al-wadud is the woman who shows affection to her husband. The Prophet, peace and blessings be upon him, greatly emphasized the husband's rights over his wife and warned her against disobeying or angering him. This does not contradict the opinion of those who say that a woman's affection towards her husband might lead to her neglect, because that only happens if the husband is mean and ill-mannered, and Islam encourages marrying a person of good character and religiosity.