Accusative case

The accusative case is the grammatical case which marks the direct object of a transitive verb. This is best explained with examples:
Forms.
In the sentence ""He" sees the woman", "he" is the subject of the sentence. In the sentence "The woman sees "him"", "him" is the object. 
English.
So, in English we use different forms of the pronoun: he/him. "Him" would be the accusative case. If we use a noun, there is no difference in English. We use the same word "man": The man sees the woman" and "The woman sees the man. 
In many languages different forms of the word are used, depending on what function it has in the sentence - subject or object. 
Latin.
For example, in Latin. "The man sees the woman" = "Vir feminam videt", while "The woman sees the man" = "Femina virum videt". For "man", Latin uses "vir" for the subject, and "virum" for the object. Also, in the same sentences, we have "femina" for a subject and "feminam" for object. The form used for the direct object ("him", "virum", "feminam") is known as the "accusative case", while the form used for the subject ("he", "vir", "femina") is known as the nominative case.
German.
In some languages, like German, the accusative case is applied to the definite article and not to the noun. In German, "the car" as the subject of a sentence may be "der Wagen". This is the form in the nominative case. When "the car" is used as the object in a sentence, it becomes "den Wagen", the accusative.