In English, sentences can have something called an 'object complement.' This is a word or group of words that gives more information about the object of the sentence. Think of it as a way to tell more about the object and how it is changed or affected by the action of the verb.
In these examples, 'brilliant,' 'president,' and 'blue' are object complements. They tell us more about the student, her, and the house, which are the objects in each sentence.