What is meant by a grammatical case in Latin (e.g. Nominative, Genitive, Accusative)?

The grammatical case system in Latin can be an extremely confusing concept for English speakers because in English, meaning is usually determined through word order alone or, occasionally, when prepositions are used. For example, take the sentence: The cat chases the dog.  We know that is it is the cat who is doing the chasing because its name appears before the verb - it is the subject of the sentence and is the one who is doing the action - there is no other way of conveying this meaning in English besides this word order. The dog is the direct object since it is the one that is the recipient of the verb ie the dog is being chased.  
In Latin, in order to convey meaning there is something called 'grammatical case' whereby a noun will have different endings according to its function in a sentence (ie whether it is the subject or object of the sentence). Latin has SIX grammatical cases to reflect this.  So, for the above sentence:·     The Nominative case is used for the subject of the sentence (ie the cat would have a Nominative ending in Latin), whereas ·     As the dog is the object, it would go into the Accusative case. ·     The Vocative case is used in direct speech when addressing something/someone, for in the example, 'cat, come here!' the 'cat' would go into the vocative case. ·     The Genitive case indicates possession.  In English, this is often indicated through an apostrophe. In the example, the cat ate the dog's food, it helps to think of this as the food of the dog, so here the dog would go into the genitive case. ·     The Dative case is used for the indirect object, for example, the cat gave his food to the dog. In this instance, the dog would go into the Dative case as it is the indirect object (because, note: it has the preposition to, making it indirect), whereas 'food', as the direct object would go into the Accusative. ·     Finally, the Ablative case is used when in English we say 'by, with, from something', for example, the dog was terrified by the cat; here the cat would go into the Ablative case in Latin.