I wear a modest hat to mass mostly except at adoration sometimes a veil because I usually have it handy in my purse ( can't stuff a hat in my purse:D).
Head covering is a personal devotion that I ( and many Christian women these days, not just Catholic) have felt called to in varying degrees AND struggled with, questioned and fought against, and sometimes treated quite rudely for ....trust me.
I once asked a priest at a women's conference where on earth this urge was coming from since I am not a cradle Catholic nor do I or have I ever had anyone suggest it to me, and there are perhaps only 3 people in my parish of 2000 families that wear a veil. He said it was a good thing and not to be afraid of it. That I should get to know Mary better.
For me the explanation that I heard about something to do with the mass, that did not even address women's head coverings, sealed the deal for me.
The cliff notes are : All glory is given to God and focused on God at mass, we should attend mass with a humble heart. Hence if women's glory is their hair ( no wonder we spend so much money and time on it!) and the glory of a man is his wife then in order for the woman AND man to not have anything to 'boast' about as they participate at mass , a woman - out of respect and honour for God , should cover her head (or shave it I guess!) .
Sorry I am lousy with the scripture references but the revelation came to me while I was doing a Scott Hahn, St Paul's Center for Biblical Theology study ; either A Father who keeps His promises or The Lamb's Supper. Let me make it VERY clear - no where in this study did they say women HAD to cover their head , nor did they even say they should- if they even mentioned it at all.
This is a private devotion in a sense.
Since this revelation I have realized how ironic it is that women in society usually cover their heads when they loose their hair.....makes you wonder if that isn't because of the ancient connotation of a woman with no hair?
Hope this helps.
The different colors really mean nothing any more in the old days I think that black was for married women and white for un-married for obvious reasons.