Waving and Covering the Eyes
It is customary for women to wave their hands and then cover their eyes when reciting the blessing upon the Shabbat candles. The reason for this is to comply with the halachic principle that a blessing must precede the performance of a mitzva, and not the reverse. Contrary to popular misconception, the lighting of the candles is only one component of the mitzva of Shabbat candles. The mitzva is only completed when one has derived benefit and enjoyment from them, as well. As such, a woman covers her eyes immediately after having lit the candles in order to avoid deriving any benefit from the light until she has recited the blessing.[1] In this way the blessing over the Shabbat candles is still deemed as having been recited before the completion of the mitzva. After the blessing is recited the hands are removed from the eyes in order to allow her to now enjoy and benefit from the candles' light.
The waving motions evolved as an act which symbolizes the preparation for deriving benefit from the candles. It is also said to be a motion which represents accepting the Shabbat queen. According to kabbalistic teachings the soul has five components, three of which are "internal". The three wavings, therefore, represent the internal acceptance of Shabbat.[2] There also exists a custom to only perform the waving of the hands but not to cover one's eyes.[3] It also might just be that the original custom was for women to cover the candles before reciting the blessing and not their eyes. As the custom of lighting more than the required two candles became widespread, making it difficult to cover many candles with one's hands, the custom became to cover one's eyes instead.[4]
It is interesting to note that according to Ashkenazi custom, once a woman recites the blessing over the Shabbat candles she is considered to have accepted Shabbat upon herself, even though there still may be quite some time before sunset.[5] It is also for this reason that a woman first lights the Shabbat candles and only afterwards recites the blessing. Indeed, if a woman recited the blessing before lighting the candles she may then be forbidden to strike a match due to having "accepted" Shabbat through the recitation of the blessing!
Sefardic authorities dismiss these concerns and it is actually widespread Sefardic practice to first recite the blessing and only afterwards to light the candles. According to both Ashkenazi and Sefardic practice a man who lights the Shabbat candles always recites the blessing before lighting the candles.[6] This is because a man does not automatically "accept" Shabbat through the lighting of the Shabbat candles, but rather, in the course of the prayers or other declaration.
[1] Rema O.C. 263:5
[2] See: http://www.shamash.org/lists/scj-faq/HTML/faq/07-08.html
[3] Rivevot Ephraim 2:115:64
[4] Rivevot Ephraim 1:183, 4:67
[5] Rema O.C. 263:5
[6] Mishna Berura 263:42