The obvious is G-d. There is only one G-d. There is only one sun and moon and earth and universe for us. Only one people called the Jews and only one Eretz Yisrael. There is only one Torah though many ways to understand and dig deep.
One is the smallest real number that has value but usually implies power. There is only one king, president or César. There can only be one boss or captain. We have only one head, one mind, one heart.
One is unique, special and irreplaceable.
We have only one mother and one father. That is why if one is sitting shiva for the death of a parent it has a longer consequence than other relatives. Spouses can be replaced (at least in the sense a person can remarry). There can be numerous brothers and sisters and even other children. But there can only be one mother and only one father; so one needs to mourn (keep the laws of mourning) for parents for a year; while every other relative a month is enough.
One can be the unity of many parts that unify and recognize their companionship and connection enough to be called one. United States, United Kingdom are examples of this phenomenon.
There can only be one first born and only one youngest. There can only one pideon haben and one broom dancing ceremony for the last child to get married.
And there can only be one of you and one of me. We are all unique and can be called the one and only.