The objective case is a grammatical case for nouns. A word in the objective case serves as a direct object of a verb or preposition.
objective
2. Gram.
a. Also called objective case. (in English and some other languages) a case specialized for the use of a form as the object of a transitive verb or of a preposition, as him in The boy hit him, or me in He comes to me with his troubles. http://www.infoplease.com/ipd/A0563439.html
English doesn't pay much attention to case except for pronouns. As Ron said, if a pronoun is the subject of a sentence or clause, we use nominative case pronouns: I, you, he/she/it/, we, they, who. If a pronoun is the object of a verb or preposition, we use objective case pronouns: me, you, him/her/it, us, them, whom.