A noun is expressed in the nominative case when it is used as the subject of a sentence. Subjects are usually placed at the beginning of a sentence in English, so this case basically tells where the noun appears in a given sentence. An example is the following sentence, "The dog barked all night." The noun "dog" is found here in its nominative case.
A noun expressed in the objective case is used as the direct object in a sentence. An example is found in the following sentence, "I ate the sandwich." The noun "sandwich" is used in the objective case as the direct object of the sentence. As can be seen, there is no difference in appearance between the nominative and objective cases. In these situations, a noun's case simply indicates location in a sentence.
The possessive, or genitive, case of a noun indicates possession. An example is found in the following sentence, "She cleaned the dog's house." The noun dog's is a possessive case noun. The possessive case is indicated by the addition of an apostrophe and an s.
Other cases exist, but their form is identical to the nominative. For instance, the dative case indicates that the noun is an indirect object. An example is the following sentence, "We gave the dog a bone." In this sentence, "dog" appears in its dative case. But, as with the objective case, the word's form remains the same.