The NOAD installed on my Mac Mini reported the following definition for pray .
adverb formal or archaic used as a preface to polite requests or instructions: pray continue .
• used as a way of adding ironic or sarcastic emphasis to a question: and what, pray, was the purpose of that?
In the first example, you can replace pray with please .
Similar definition is given by the Oxford Living Dictionaries .
english.stackexchange.com/users/252/kiamlaluno
http://www.etymonline.com/index.php?term=pray pray late 13c., "ask earnestly, beg," also "pray to a god or saint," from O.Fr.
preier (c.900), from L. precari "ask earnestly, beg," from *prex (plural preces, gen. precis) "prayer, request, entreaty," from PIE base *prek- "to ask, request, entreat" (cf.
Skt.
prasna-
, Avestan frashna- "question;"
O.C.S. prositi, Lith.
prasyti "to ask, beg;" O.H.G. frahen, Ger. fragen, O.E. fricgan "to ask" a question).
Parenthetical expression
I pray you, “
please, if you will,” attested from 1510s, contracted to pray 16c.
english.stackexchange.com/users/2022/mplungjan
The word "pray" means to earnestly ask something of someone.
Therefore, the phrase "pray proceed" could be interpreted as "Please, I beg of you, proceed".
In modern English, we often think of the term "pray" in a spiritual context, but the meaning is the same: to ask something of someone.
english.stackexchange.com/users/4193/Andrew
See also the version I like enough to consider using in conversation to stage a come back: Prithee tell .
The etymology sheds some light on the sometimes sarcastic nature of pray tell .
english.stackexchange.com/users/4204/Ashley
adverbformal or archaic 1Used as a preface to polite requests or instructions: ladies and gentlemen, pray be seated 1.1Used as a way of adding ironic or sarcastic emphasis to a question: and what, pray, was the purpose of that?
From online Oxford English dictionary
english.stackexchange.com/users/97131/david
Is this an archaic form of "please proceed"? I have never heard in in speech but sometimes it appears in novels. My version of "The Adventures of Sherlock Holmes" is full of it, apparently in place of "please".
What does "pray" mean in phrases like "pray proceed"?
english.stackexchange.com
<meaning><phrases><archaicisms>
english.stackexchange.com/questions/10057
english.stackexchange.com/users/544/Tamás
The word "pray" means to earnestly ask something of someone, and therefore, the phrase "pray proceed" means "please proceed". The word "pray" means to earnestly ask something of someone. It is an archaic form of a polite request. In modern English, we often think of the term "pray" in a spiritual context, but the meaning is  to ask something of someone.Therefore, the phrase "pray proceed" could be interpreted as "Please, I beg of you, proceed".   It can also be used as a way of adding ironic or sarcastic emphasis to a question: and what, pray, was the purpose of that?  
The word "pray" means to earnestly ask something of someone, and therefore, the phrase "pray proceed" means "please proceed". This is an archaic usage that could be considered synonymous with 'please', although in modern usage it is often intended to add ironic or sarcastic emphasis.
The word "pray" means to earnestly ask something of someone. It is used as a preface to polite requests or instructions:  pray continue .    The word "pray" in this context means "to politely ask something of someone". 
The word "pray" means to earnestly ask something of someone.
The word "pray" means to earnestly ask something of someone. It is an archaic form of a polite request.
This is an archaic usage that could be considered synonymous with 'please', although in modern usage it is often intended to add ironic or sarcastic emphasis.
The word "pray" in this context means "to politely ask something of someone". 