An object is a part of a sentence that represents the noun on which the action is taking place.
Sara don’t like Adam at all.
In the above example, Adam is the object as the action is taking place on him.
An object that is etymologically related to the verb of the sentence is known as a cognate object.
He was singing a song.
Song is the noun and sing is the verb and they are both etymologically related so song will be called the cognate verb.
In other words, when a verb and a direct noun of a sentence are both similar in form and meaning to each other, the object is termed as cognate object.
He dreamed a horrible dream.
In the above sentence, dreamed is the second form of the verb dream and the direct object dream is similar in form and meaning to the verb. Thus direct object dream is called cognate object.