can you guys give some examples of what you're talking about?

Yeah, sure ... Take Latin. Nouns are declined for case and number. For every noun, you have upwards of 10 forms (for two numbers, singular and plural, and 5 cases, nominative, genitive, dative, accusative, and ablative). Here's a paradigm for two nouns:

NS :- puella 'girl'
GS :- puellæ 'of the girl, the girl's'
DS :- puellæ 'to / for the girl'
AS :- puellam 'the girl'
AbS :- puellâ 'with / by a girl'
NP :- puellæ 'the girls'
GP :- puellarum 'of the girls, the girls''
DP :- puellis 'to / for the girls'
AP :- puellas 'the girls'
AbP :- puellis 'with / by the girls'

(NB on the translations, Latin has no articles, either definite or indefinite, so you could say puella means 'girl, a girl, the girl'.)

So, that's what we mean by case endings (e.g., -a, -æ, -am, -arum, -is, and -as in this case). Case is used to show the syntactic relationship between a noun and another noun or a verb. For example, puer puellam amat means "The boy loves the girl". So does puellam amat puer, or any other combination of the three words. (Though note that some orders of the three words are more common than others.) Unlike say English or Chinese where word order shows the syntactic relationships between words in a sentence, in inflected languages (like Latin, Russian, or Sanskrit) it's the case endings. So, nominative is usually the (grammatical) subject of a sentence, accusative the direct object, and dative the indirect object. (NB, this is a simplsitic example. Cases have different meanings (when translated) and uses.)

So, what about prepositions? Latin had 'em. Take two of them: post 'behind' and prae 'before, in front of'. When post is used with a noun, the noun must be in the accusative case, and when præ is used, the noun must be in the ablative. This is what is meant by a preposition governs a certain case.

OK, let's bring in history. What happened to Latin when it changed, over the years, into Italian, Spanish, Portuguese, Catalan, Provençal, French, Romanian, Sardinian, Friulan, et al.? Lots of stuff changed. But what we're interested in is case. Well, cases disappeared, and were basically replaced with word order. (NB: the same thing happened in English and Danish, but not in German. They are thought to be descended from a single Common Germanic which never got written down but probably existed back around the time of Latin or earlier.)

Not all grammatical categories disappeared: e.g., number stuck around and in verbs tense, person, etc. made it through. Let's look at the Spanish and Italian words for girl:

Italian
sg :- una / la ragazza 'a / the girl'
pl :- le ragazze 'the girls'

Spanish
sg :- una / la muchacha 'a / the girl'
pl :- las muchachas 'the girls'

Some stuff to notice: the lexemes (fancy word for word) have changed: puella, ragazza, and muchacha; the endings have changed, both the newer words end in -a but the plurals are different in Italian and Spanish; no more multiple cases like in Latin.

Now the question Faldage and I were mulling over is this. How / why did the changes occur? Or where did the cases go and why? As I said, it's not something that has to happen, see German and Russian, but it does, see English and Italian.

It is thought that spoken Latin, say in Cicero's time, was different from written Latin. The distinction between nom sg puella and acc sg puellam was disappearing. First the final m was reduced to nasalization of the preceding a, and finally it went away. Now nom and acc could be confused, but only if you used some weird word order rather than the one that was most common. (Even though, the common word order of latin SOV became Italian's common word order SVO; where S == subject, O == direct object, and V == verb. Now how did that happen?)

Anyway, eta, I think that's most of the jargon, but if you have any more questions please ask away ...