I wear a headcovering because I feel we are told to as Christian women in 1 Corinthians.
1 Corinthian 11:1-16~Be ye followers of me, even as I also am of Christ. 2~Now I praise you, brethren, that ye remember me in all things, and keep the ordinances, as I delivered them to you. 3~But I would have you know, that the head of every man is Christ, and the head of every woman is the man; and the head of Christ is God. 4~ Every man praying or prophesying, having his head covered, dishonoureth her head: for that is even all one as if she were shaven. 6~ For if the woman be not covered, let her also be shorn:but if it be a shame for a woman to be shorn or shaven, let her be covered. 7~For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man. 9~ Neither was the man created for the woman, but the woman for the man. 10~For this cause ought the woman to have power on her head because of the angels. 11~Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord. 12~For as the woman is of the man, even so is the man also by the woman; but all things of God. 13~Judge in yourselves: is it comely that a woman pray unto God uncovered? 14~ Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him? 15~But if a woman have long hair, it is a glory to her: for her hair is given her for a covering. 16~But if any man seem to be contentious, we have no such custom, neither the churches of God.
I had always believed, as I was raised, that the headcovering was the hair, but after feeling convicted by the Holy Spirit I studied the scriptures in depth. Just reading the verses the way they are written shows me that the hair isn't the covering Paul was referring to. There are two different Greek words that are translated in KJV as covering. Verses 4-14 use the Greek word katakalupto. This word means to cover wholly i.e. hide, cover, veil. Verse 15 on the other hand uses the word peribolaion which means something thrown around one, i.e. mantle, veil, covering, vesture.
Mainly though, I cover 1) Because I feel God told me to, 2) To show submission to my husband, and my Saviour, and 3) I cover all the time, so that I am not without a covering whenever I feel the need to pray or worship.