In Latin and Greek, as in other inflected languages, there are multiple forms for each noun to signify the role the noun plays in the clause or phrase. One form of the noun is used as the singular subject; another as the plural. So much we also have in modern English, where the two are usually differentiated by "s". Actually, English has 3 such differentiations or cases: subjective, possessive, and objective.
In more highly inflected languages there are other forms, too.
What distinguishes the various cases (forms) from one another in Latin and Greek is the ending on the noun, which goes on the stem, so they are called case endings.
In Latin and Greek there is a set of endings for the singular and another for the plural. (Greek also has a dual case.) Latin has five complete sets of case endings. These are known as the five declensions.
The nominative is sometimes called "upright" (rectus, in Latin); while the other cases are called "oblique". The word "case" comes from a Latin word signifying "fall" as if the word falls from its straight up nominative form to go through the other forms.
The case endings are translated into English with the help of prepositions or an s with an apostrophe.
More on Latin Cases
Examples:
Urbs, a 3rd declension noun, is the nominative case singular of the Latin noun for city.
Stem: urb-.
Urbis is the genitive case singular, translated as "of the city".
The dative case singular is urbi, translated as "to/for the city".
The accusative case singular is urbem. Urbem can be the direct object of a verb or the object of a preposition.
The ablative is urbe, which can be translated by various prepositions, but might be translated "with the city".
The plural of urbs also has case endings for the nominative, genitive, and accusative that are distinct. The ablative and dative plural are the same.