What is the significance of the "thou" often used when English speakers address God?
(What follows is pure speculation on my part.)
Let's start with the grammatical first person.
We are all familiar with these words. What's important is to note the difference between singular and plural. Example sentences:
Let's skip the second person and look at the third person.
|Nominative||I||we||she / he||they|
|Accusative||me||us||her / him||them|
|Possessive adjective||my||our||her / his||their|
|Possessive pronoun||mine||ours||hers / his||theirs|
These also are familiar to us. Again, singular and plural forms differ. Example sentences:
We go now, not to the second person as we use it today (which does not distinguish between singular and plural), but to the second person as it was used in much older times, in for example the times before Shakespeare. (Shakespeare of course lived during the time the King James version of the Bible was being prepared, and it is that version of the Bible that has had the greatest impact on the way language is used in religion in English.)
|Nominative||I||we||thou||you / ye||she / he||they|
|Accusative||me||us||thee||you / ye||her / him||them|
|Possessive adjective||my||our||thy||your||her / his||their|
|Possessive pronoun||mine||ours||thine||yours||hers / his||theirs|
There's a column there that is unfamiliar to modern English speakers, but which is probably familiar to anyone who reads Shakespeare or the King James Bible. In older versions of English, there was a set of pronouns for use with the singular, which sound archaic now: "thou, thee, thy, thine".
What apparently happened was, as a result of the dominance of Middle French in England in the centuries following the Norman Conquest, English speakers adopted the French practice of using the second person plural ("vous / you") in place of the singular ("tu / thou") in order to show respect or distance, as to a stranger or social superior. To people above you on the social ladder, or to people who you did not know well, you'd use "you" (just as in French you'd use "vous"—which was originally the plural, but also came to be used in this way for the singular). To people below you in the social hierarchy, or to intimate acquaintances, you'd use "thou" (similarly to the French "tu").
Accordingly, if you were to say to your lover, "I love you", she/he would be offended. "Why are you being so cold to me?" he or she would ask. "Don't treat me like a stranger. Say 'I love thee' or don't say it at all."
Conversely, if you were to approach a stranger in the street and say, "Who art thou?" you might get a punch in the nose. To someone you don't know, "thou / thee" would be presumptuous. Ask "Who are you?" if you want to stay on the right side of courtesy.
What does this have to do with religious language? We should ask again: why does religious language in English refer to God with "thou / thee / thy / thine" and associated archaic grammar?
Some people might assume that it's "old English" and that this is used in religious speech for the sake of tradition, or to make things sound stuffy and important. And perhaps there is some truth to this. The King James version of the Bible was in fact written in a style that would have seemed a bit old-fashioned to contemporary readers, and this was done on purpose, to make it sound 'traditional'.
But in fact, there is also a deeper significance. It helps to remember that the King James version of the Bible was assembled in a time when England was officially Protestant, and that the Protestant ideal of the individual's direct relationship to God, for which the mediation of the Church was not required, would have been most current.
To call God "thou, thee" etc. would then take on a particular significance. Of course, there can be no question of referring to God as a social inferior—one of the uses of "thou" etc.—so the other nuance must obtain, that of an intimate relationship.
Bet you never thought about that.