"Modest' for the Bat Israel (Woman of Israel) means to dress 'not frumpy' but with elegance to fulfill their Tznuit (modesty) and bring their husbands joy. Here is a site with samples of their apparel and styles, including headcoverings. This site on orthodox Jewish dress includes both men and women.
"Modest" for some Christian groups has also meant wearing caps, veils, and scarves as seen here. Some are protestant groups based in the Reformation and others are Catholic. The LDS church also has very specific dress guidelines for modesty. For others, it is a recent adaptation as seen here in a business that opened in 2002. They cite adopting the action in obedience to 1 Corinthian 11:1-16. For other groups, being modest has meant plain dress, no makeup, no jewelry, long skirts, and long hair. Some younger women are changing this to emphasis more style while retaining the modesty.
"Modest" for Islamic women includes the scarf (Khimar), the total body covering (Hijab), and the face veil for the most devout (Niqab). You can read some rather detailed explanations of the rationales for wearing each and how they relate to worship by the devout Islamic woman here. This site also, interestingly, reveals the dress codes for men to be considered modest within Islam.
Note, I could find no major websites addressing what it meant to be modest if a Christian man.
What is modesty? In practical terms it is keeping revealed by clothing various parts of the human form which are deemed "private", "titillating", or "unseemly". Thus, the breasts, arms, legs, hips, face, and head/hair are variously in need of coverings. No underwear may be seen through sleeves, no cleavage, and nothing too tight or form fitting to bring attention to the attributes marking the gender. The primary belief among modest Christians is that the good deeds and faith will be the makeup and ornamentations of beauty.
Many will agree modern society has become extreme in its dress and fashion. The human form is constantly on display to promote sales, to evoke sexual thoughts, and to provoke interest. Dance moves have become often mere grotesque pelvic thrusts and bizarre gyrations mimicking animal lust rather than graceful, joyful, or meaningful movements to music. Sexual encounters, references, and acts are seen as part of the normal entertainment cycle in books, music, movies, and on television. Children are being sexualized at earlier and earlier ages. Women have become liberated and yet abuse of women continues. Prostitution a growing business and sexual affairs commonplace. People wear veils, headcoverings, and long hair. They dress in long sleeved dresses and wear no makeup but has that impacted the world for good? Is there any evidence that those exterior 'things' have in any way helped the world, spread the gospel, feed the hungry, aided the poor, or soothed the hurting?
Will being 'modest' alone impact this sorry state of affairs? Will retreating to communities or rural areas living a modest life make changes? Will legalistic-ally demanding compliance to a set of rules as to length of hair, cutting of hair, type of head covering, sleeves or no sleeves, really mean anything in the long run?
If it is really between a woman and her God....it should be between a woman and her God. Her liberty should be to adopt the custom or not with NO outside interference or demands by religious groups.