I've just got home from church and I still smell of incense because I was thurifer (the person who takes charge of the incense) this evening.
In the Gospels there's a story of a woman who anoints Jesus with costly perfume in order to honour him. Using the perfume on him was a sacrificial offering because of how expensive it was, and by the act she demonstrated how highly she thought of Jesus. (At the end of the story we're told that the fragrance filled the house.)
I think there's something of the above in why we use incense in church. God is so worthy of our praise that we want to perform loving and generous gestures that show how highly we honour Him. There's a tradition of the Roman Emperor having incense burned ahead of him in procession as a way of him being honoured (actually, they were saying by the incense that they recognized he was divine!). The incense is used at certain points in the Eucharist and directed towards certain objects and people as way of honouring those objects / people / moments in the service, and saying how spiritually important they are. The altar is censed because that's where Jesus will be present in a very special way. The Gospel book is censed to honour Jesus, the Living Word, who is encountered in the reading of the Gospel.
As well as honouring a person or object, incense signifies a 'setting apart for God's purposes'. For example, the bread and the wine are censed because they're being offered to God. The congregation are censed as an acknowledgment of them being God's holy people, and because they're also being offered to God for his purposes.
In the Bible, incense is strongly linked with prayers rising to God. God instructs the Israelites to use incense in their worship. The Psalms and the book of Revelation talk of prayers rising like incense to God.
When you watch the clouds of incense rising, it's like watching our prayers rising up. That leads to another part of the symbolism - incense 'pointing out' things that are invisible. Lots of spiritual things are invisible - our prayers, Christ's presence, the holiness of things that look ordinary. There's a verse in the Bible that talks of the fragrance of Christ filling this place. The smell and the sight of the incense remind us of how present Christ is in the building, particularly in the Gospel and at the altar in the Holy Communion. Also, although Christians tend to look quite ordinary, we're made in God's image, we've received God's grace, God has made us a holy people and put his own Spirit in us. Things like robes and incense remind us of our holiness and how we're citizens of Heaven, as normal as our lives might look and feel.
