The yamaka is a thin, slightly rounded skullcap which is worn by Orthodox Jewish men at all times. This particular hat may also be worn by both men and women during services, particularly in Reform and Conservative communities. The yamaka is worn to show someone's admiration and honor towards God.
Yamaka is a modern, misspelled and mispronunciation of the term used to refer to this religious headpiece. The real name for the hat was supposed to be a kippah, or a yarmulke. It's the latter word that the term yamaka came from, since yamaka is a poorly pronounced version of the word yarmulke.
The wearing of a yamaka can be found in what Christians would call the Old Testament, in the Talmud. In Shabbat 156b, the writing states, "Cover your head that the fear of Heaven may be upon you." While a yamaka may be worn at all times by custom, it is generally agreed upon by many Jews that it is only truly necessary when they are praying.