In Old English, thou (thee, thine, etc.) was singular and you was plural. But during the thirteenth century, you started to be used as a polite form of the singular - probably because people copied the French way of talking, where vous was used in that way. English then became like French, which has tu and vous both possible for singulars; and that allowed a choice. The norm was for you to be used by inferiors to superiors - such as children to parents, or servants to masters, and thou would be used in return. But thou was also used to express special intimacy, such as when addressing God. It was also used when the lower classes talked to each other. The upper classes used you to each other, as a rule, even when they were closely related.
So, when someone changes from thou to you in a conversation, or the other way round, it conveys a different pragmatic force. It will express a change of attitude, or a new emotion or mood.
David Crystal, “The Language of Shakespeare” — as included in The Oxford Shakespeare: The Complete Works, Second Edition.
I found this incredibly fascinating and informative, in regards to the difference between the Old and Middle/Modern English “thou” and “you” forms.