I have always been under the impression that people wear their talises over their heads when davening as their second head-covering. I understood this to be the reason why people don't wear black hats when davening shacharit.
But I commonly see people who do not wear a black hat (including when davening mincha and ma'ariv) who still cover their heads with their talis during shacharit. What is the reason that these people do this?
The Mishna Brurah 8:4 brings the Bach who holds one should cover the heads with the tallis which brings yiras shamayim.The Mishna Brurah in hilchos hikon tefillah(I think siman 91,or 90,he brings that one should cover his face with the tallis during shemoneh esri.There are numerous sources which say to cover the head with a tallis.The Ben Ish Chai in Hilchos tzizts writes those who don't cover their heads with a tallis during the hot months are not doing correctly.
The custom was once that the talis was the main garment a man wore. While that is obviously not the case anymore, we do wear a talis katan (small talis) to keep the mitzva of tzitzis with us the whole day. (It is a shmira - reminder or spiritual protection against forbidden relations.)
However, it is highly questionable if a regular talis katan1 fulfils the Torah's requirement of a real garment - one that can cover the body properly - and it therefore became practice to wrap (ituf) one-self in a proper talis (called talis gadol - large talis) once a day. The time chosen for this was set to be that of shacharis, which is the most elaborate and foundational prayer of the day.
Our days' talis therefore has a special elevated status, being both the full-scale performance of a Torah mitzva, and also a garment set aside for the holiest time, i.e. prayer. (That is why we do not wear it for Tisha B'Av shacharis - as a sign of mourning.) The talis is used as a sign of higher status: To carry a Sefer Torah. By the one leading mincha. Yom Kippur by night, and the whole day too. To enhance this mitzva, many decorate their taleisim elaborately with silver plates or woven bands.
When wearing a talis, it is customary to hold on to the talis even beyond shacharis: On Yom Tov, mincha is sometimes prayed right after shacharis (before the meal) in which case many keep the talis on for mincha too. Some keep it on until after Shabbos day kiddush. If shacharis is followed by a bris mila, many will keep their tallis on for this too.
Finally, some may find that their concentration is enhanced by using the talis to shield off the world during prayer.
1. A very large and long talis katan in accordance with the Gr"a may.
The Taz in hilchos tzitzis says that we wear a yarmulke even when the tallis is covering the head in case the tallis slips off. It would seem that if not for that concern, one would take off their yarmulke when wearing a tallis, and there is no need for a double head covering. There are poskim who require atifas harosh (surrounding the head, not just having something on top of it) for Shemoneh Esrei, and particularly for Kedusha, because it is a davar sheb'kedusha (this is also accomplished by a hat of any color). However, the Bach cited by Mishna Berura brings that one should wear the tallis for the whole davening, which would require a reasoning beyond that which applies to shemoneh esrei.
