Vulgar Latin is an early evolution of Latin that appeared in Italy from the 8th to 13th centuries. It represents the evolutional bridge from Latin to modern Italian, French, Spanish, etc.
Its origins are due to the fact that Latin was (and is ..:-) the official language of Catholic church, and maybe non-learned people tried to use it.
Not at all - it comes from the Latin spoken by commoners during Roman times.
Vulgar Latin is more of an umbrella term for the various Latin dialects spoken in the provinces of the former Roman Empire. These dialects were rarely written; their users, if they could write at all, wrote in the more formal classical Latin, or the prevailing language in the area (e.g. Arabic in medieval Spain). The vulgar dialects gradually evolved to the point of mutual unintelligibility (speakers of dialect A could no longer understand dialect B, and vice-versa), and depending on political circumstances, either evolved into national languages (Spanish, Italian, French), minority languages (Sardinian, Catalan, Gallego), or died out (like Mozarabic, a vulgar dialect of southern Spain which was heavily influenced by Arabic).
Proto-Indo-European circa 5000 B.C.E had 8 noun cases; its descendent, classical Latin, largely merged the locative into the ablative, and lost the sociative-instrumental (means/agency), leaving it with six full-fledged cases:
Medieval Church Latin had only 3 noun cases, Old French had only two, and most modern Romance languages have none at all (except in the pronouns, as is also true in English).
BTW people still talk about long and short vowels in English, too, confusing almost everyone. The terminology refers to the length of time that a vowel is pronounced - yet there is no such distinction in modern English. But there once was; it was lost in the "Great Vowel Shift", and replaced by contrasts of different related vowels. Yet the terminology "long and short vowels" was retained. -- DougMerritt
The "a" in "take" is referred to as long, and that in "tack" is short. However, duration is a separate issue - there is a slight timing difference between "band" and "banned", and also "jam" and "ham" have subtle timing differences, depending on their meaning.
Any clearer examples?
It's a difficult subject, in part because there is some disagreement between different camps.
My favorite camp says that there really isn't any long versus short vowel distinction remaining in English at all; instead, there are stress distinctions, so that you can tell the difference between the sound of "band" and that of "banned" because the latter is more highly stressed.
But what is "stress", exactly? Well, it varies, and it's extremely hard to be completely rigorous about, but native speakers always know it when they hear it: it is a marking of amplitude, frequency, meter, duration, etc compared with the usual unmarked case. So the initial vowel in "banned" might have longer duration than in "band" -- or it might instead be pronounced louder or with some other kind of emphasis.
You'll know that the theory of Prosody is pretty mature once you start hearing voice synthesizers pronouncing novel sentences just like humans do. :-)