One will readily notice that wearing a hat and jacket during prayer is standard dress in many orthodox circles. It is generally assumed that the reason for this is to comply with the requirement to be dressed “appropriately” when standing before God in prayer. In fact, it is especially meritorious to have a garment reserved exclusively to be worn during prayer and a hat can often conveniently fill that role.
In earlier times, wearing a hat and jacket was standard dignified dress for both Jews and Gentiles. In some locales it was considered virtually inappropriate to appear in public without them. As such, the halachic authorities who lived in such places ruled that one must wear a hat and jacket when praying in order to conform to the requirement to wear standard dignified clothing when praying. It was reasoned that if one is particular to wear a hat and jacket when appearing before important people, then one should wear such clothes when appearing before God, as well. Further support for wearing a hat was taken from the example of the Kohen Gadol who was required to wear a hat when officiating in the Beit Hamikdash.
More recent halachic authorities, however, recognize that wearing a hat and jacket is not necessarily the normative style of dress today. In our day, most people are not particular to be dressed with a hat and jacket when leaving their home, nor is such attire required when meeting important people. In fact, in some countries, appearing before figures of authority while wearing a hat is actually frowned upon.As such, any former requirement to be dressed in a hat and jacket when praying has simply fallen dormant in most orthodox circles.
Some authorities argue that although wearing a hat is no longer the common manner of dressing today, one should still consider doing so for purposes of added modesty. Wearing a hat is also considered by many as complying with the recommendation that one’s head should be completely covered during prayer especially when reciting the Birkat Hamazon, though a large kippa would satisfy this view, as well. It is also interesting to note, however, that today’s definition of formal or dignified attire certainly calls for the wearing of a tie and yet there is no demand from contemporary halachic authorities to do so for prayer. As such, it can be derived from here that the criterion of how one must dress for prayer is not necessarily related to conventional or even ceremonial protocol.
As the consensus of most contemporary halachic authorities is that there is no true obligation to wear a hat or jacket when praying, doing so has become more of a sign of social affiliation than anything else. The halacha simply requires one to dress for prayer in the same manner one normally dresses when appearing in public forums. One who is particular to only appear in public forums while wearing a hat and jacket is required to do so for prayer, as well. There is no need to dress for prayer any differently than one’s standard method or style. Other authorities measure the standard for dress during prayer as the manner in which one would dress when appearing before secular or Torah authorities. This too, leaves the matter open to a subjective interpretation – not a communal one.
Even though most of the original reasons for requiring a hat and jacket for prayer are no longer relevant, it may just be that the reason the practice continues in certain circles is simply due to an inherent hesitation to change any practice even when new realities completely justify such changes. Even those authorities who generally require one to wear a hat a jacket when praying acknowledge that ultimately what one wears has little significance, and what matters is one’s attitude, reverence, and concentration during prayer.
******************************************* Shabbat 10a, Amos 4:12
 O.C. 98:4
 Chayei Adam 22:8, Mishna Berura 91:5, Aruch Hashulchan 91:5
 Melamed L’hoil 56
 Mishna Berura 46:9
 Rambam Tefilla 5:5, O.C. 92:6
 Berachot 51a, Kitzur Shulchan Aruch 44:6
 Minhag Yisrael Torah 2:6, See also Tzitz Eliezer 13:13
 Shaarei Halacha 18
 Aruch Hashulchan O.C. 95:6, Sheilat Shlomo 2:233, 4:25
 Mishna Berura 91:12
 Shevet Halevi 10:18