We also see Simeon and Anna. Simeon told Mary that a sword will pierce her own soul - Jesus himself is to be the true sacrifice which will take away the sins of the world.
So Candlemas Day looks back to Christmas Day, but also looks forward to Good Friday and Easter Sunday. As a Candlemas Carol puts it so well:When candles are lighted on Candlemas Day
The dark is behind us, and Spring's on the way!
The candles invite us to watch and to pray,
When Christmas greets Easter on Candlemas Day!
I don't know about you, but I am certainly pleased at the thought that Spring is on the way!