An anthropologist correctly calls it religion, a psychologist correctly calls it relationship, but for me the essence of Christianity is the mystery of the indwelling Christ.
Some Christians want to deny it is a religion, but that is not entirely honest. No matter what identity you hold, it is impossible to avoid the anthropological dynamics. You cannot be a democrat or a republican, a teacher or a student, an American or a Korean, a computer programmer or a chef without adopting various behaviors with forms and functions motivated by various ideological concepts to connect you with that culture. So, as much as we might want to deny it, Christianity IS a religion and cannot stop being one because it will always show up in your life through forms, functions and expressed ideas.
Some Christians claim it is a relationship usually as part of the denial that it is a religion. And yes it is a relationship too. Even an atheist has to admit that the christian relates to God as if they had an ongoing relationship. Since a relationship involves mutual dealings, connections, or feelings that exist between two parties, Christianity is certainly perceived by Christians as a relationship of sorts. But that is still not what makes Christianity what it is at its most basic essence.
Christianity is the mystery of Christ in you, the hope of glory. The regeneration of the Holy Spirit the redemptive grace of God is brought to the believer through the indwelling Christ. That reality is hard to describe, hard to conceive, impossible to do so it can't be a religion in that sense. It also is difficult to relate to because in so many ways it involves God doing things from within that we neither understand, comprehend, nor are certain how to deal with. So it is more than just a relationship.
The transformation of the Christian is the result of the nurtured presence of Christ within. It results in a character that grows when allowed to but chokes when we try to control it, explain it or prove it. Who we are becoming in Christ-likeness will only happen because it will be the result of Christ within. It is this mystery that is the essence of Christianity.