'Thine' 'thou' 'lest' 'goest' 'quickeneth' 'hasten' In this day and age, you see these and other words all the time, usually in jest (there's another one) you might associate these words with something medieval, conjures up images of monarchy and armor for me. But defore the current dialect of English, there was Middle and Old English (Anglo-Saxon) which even before that spanded about a thousand years of West-Frisian....what I mean is that these ancient dialects can still be largely comprehended by most native English speakers TODAY despite their odd archaic syntax and structure, being more closely related to modern German than modern English. We all know these word and some use them in conjunction with their locale dialect at present. If you're stoned, this might present a confounding experience to some, to me, but whether I'm stoned or sober I cannot wrap my head around this. p.s - english is the only language besides the Scandinavian languages that can be understood by dialects long since extinct.
While we may not be able to define the words you listed, we are able to figure out their general meaning by observing how they are used in the sentence. Ah, this brings back memories of "context clues" in 1st grade.
One of the main reasons is that a lot of the root words in question are still used in some version. In addition, the "eths" and other "King James-isms" are just a different way of expressing tense that we still use. King James style English, Shakespearean English, are still strikingly similar to modern English. When you get into Olde English (like Chaucer) you start to experience a rather significant break, making it very hard to understand unless you are keyed into the vocabulary. English's evolution has been really tied into written literary traditions, causing it to be more solidified than languages that are more orally based (similar to Latin's lack of radical oral development). Finally, consider how divergent English spoken dialects have been while the written word has remained the same. Television has erased many of these barriers (which were far more distinct 40 years ago), but consider that folks in Scotland, England, Wales, Ireland, India, the American North-East, the American South, and the American MidWest at one point had English dialects so different that they had real difficulty understanding each other.
Context clues are a fantastic tool for comprehending the old dialects. I think one of the main reasons that the old dialects are still understood is because works that were written in the old dialects, such as Beowulf, are studied but many english speakers. But those words that you mentioned: 'Thine,' 'thou,' etc etc', are actually more Modern than you think. Shakespeare, for example, did not write in Old English but wrote in Early Modern English. Read this for a more thorough explanation. Shakespeare & Old English: Did Shakespeare Write in Old English?