Muslim men should have a collective sense of protectiveness for Muslim women as Allah says in the Qur'an, the meaning of which is:
"The Men are the protectors and maintainers of women…"
(Surah An-Nisaa, Ayah 34)
"There are three at whom Allaah will not look at (with Mercy) on the day of Resurrection:
the one who disobeys his parents,the woman who imitates men, andthe duyooth (a man who has no protective jealousy towards his womenfolk)."
[Saheeh Al-Jaami' As-Sagheer 3/74, hadith no. 3066]
To further understand the quality of Gheerah, we can look at an incident that Asmaa' radi allahu anha the daughter of Abu Bakr As-Siddeeq radi allahu anhu and sister of Aisha radi allahu anha relates about herself. Abu Bakr was a wealthy merchant and he married his daughter Asmaa' to the great companion Az-Zubayr ibn al-'Awwam radi allahu anhu who was a very poor man but a man of great piety and one of the companions who were promised Paradise. Asmaa' relates:
When az-Zubayr married me, he had neither land nor wealth nor slave…", so Asmaa' had to work very hard kneading dough, going far off to get water. "And I used to carry on my head," she continues, "the date stones from the land of az-Zubair which Allah's Messenger sallallahu 'alaihi wa sallam had endowed him and it was a distance of two miles from Madeenah. One day, as I was carrying the date-stones upon my head, I happened to meet Allah's Messenger sallallahu 'alaihi wa sallam, along with a group of his Companions. He called me and told the camel to sit down so that he could make me ride behind him. I felt shy to go with men and I remembered az-Zubair and his Gheerah and he was a man having the most Gheerah. The Messenger of Allah sallallahu 'alaihi wa sallam understood my shyness and left. I came to az-Zubair and said: "The Messenger of Allah sallallahu 'alaihi wa sallam met me as I was carrying date-stones upon my head and there was with him a group of his Companions. He told the camel to kneel so that I could mount it, but I felt shy and I remembered your Gheerah." So Asmaa' declined the offer made by the Prophet sallallahu 'alaihi wa sallam. Upon this az-Zubair said: "By Allah, the thought of you carrying date-stones upon your head is more severe a burden on me than you riding with him." (related in Sahih Bukhari)