This is an engaging assignment that asks you to think of one familiar concept through various lenses. I could envision working with the concept of "sister" for this assignment because my sister and I are quite close. Be sure to choose someone with whom you share a deep emotional connection in order to make this a bit easier.
First, let's look at those initial key words: denotation and connotation. Denotation is the literal, dictionary definition of a word. Through this lens, "sister" means a woman or girl who shares at least one parent with me. Connotation, by contrast, includes the feelings that are commonly associated with the term. When people think of their sisters, the term may conjure feelings of warmth, nostalgia, and understanding.
The next section of this assignment asks that you define the term by other means. This assignment lends itself quite easily to narration, which is a personal story that likely elicits an emotion linked to the connotation of the word. I might narrate the story of sleeping on the floor outside of my parents' bedroom for weeks when I was four years old because I was scared that I would somehow miss my sister's birth. Or I might tell the story about how my sister sat with me through a time of tremendous grief, carrying part of my emotional burden so that I never felt alone. In narration, it's important that you convey the small details of the story—the dialogue, the descriptions, and the precision in verbs. You don't want this to read like a summary. You do want the narration to convey what it truly means to be a sibling, a friend, or whichever word you choose to use.
This assignment also lends itself nicely to description. If you choose this option, you'd want to use adjectives to convey both the physical characteristics as well as the personality which embody the qualities associated with that particular relationship.
If you choose a relationship like "close friend," you might be able to use illustration to define the relationship. Can you think of a time when a friend did something for you that truly captures the essence of friendship? You might consider times when a friend has demonstrated loyalty, sacrifice, or dedication toward you. Illustrating the relationship by characteristics such as these could help you create a meaningful definition of the term.