Companionship is when you feel a sense of closeness being with another person. Your grandmother's companionship with her best friend might keep her feeling young and happy.
You probably experience companionship with your best friend or romantic partner, or maybe even with your siblings. A feeling of fellowship or togetherness is companionship — it's one of the reasons people get married or seek out like-minded friends. The word comes from companion, from the Old French compagnon, "fellow, mate, or friend," rooted in the Late Latin companionem, or "bread fellow," combining com, "with," and panis, "bread."