The blessing of the paschal candle occurs on Holy Saturday. A long and specific prayer accompanies the blessing. The Paschal candle represents the Paschal mystery, which pertains to all the things that God sent Jesus to accomplish on earth - the passion, death and resurrection. This mystery is at the center of Catholic faith and explains why the Paschal candle is lit during the Easter season. It also explains why the Paschal candle remains in the church all year long and why it is lit during very important times (baptisms and funerals, notably). It is a symbol of the very basis of the Catholic Church and beliefs.
Yet, just because the candle is lit at Easter and important times does not mean it remains lit for extended periods of time. In fact, the extinguishing of the candle is an important time as well. In order to understand the timing of the extinguishing, let’s take a look at a recent papal initiative. In 2007, Pope Benedict declared that the traditional liturgy of the Roman rite was absolutely available for use alongside the new liturgy of Pope Paul VI. The traditional liturgy had only been available on a limited basis through the 1980s and 1990s and Pope Benedict removed these limitations. Essentially, Pope Benedict was saying that, if the traditional liturgy had once been sacred, then it continued to be sacred. He also urged the use of the terms Ordinary Form of the Roman rite (newer missal) and the Extraordinary Form (traditional Latin mass). He emphasized that the Roman rite was singular, just with multiple forms.
This allowing of the celebration of both forms of the Roman rite has affected when the Paschal candle is extinguished. Some churches allow it to burn through Pentecost - the entire Easter season. In this context, it demonstrates the continuity and the wholeness of the season, which ends on Pentecost. Because the Paschal candle is moved to the baptismal after Pentecost, it also symbolizes that the Paschal is present in all sacraments.
The extraordinary form of the Roman rite, however, calls for the Paschal candle to be extinguished on Ascension Thursday. In this ritual context, the candle symbolizes the presence of the risen Christ, so it makes spiritual sense to extinguish the candle at the Ascension. It helps Catholics absorb the event of Jesus ascending into heaven as the smoke rises.
Pre-2007, almost all churches extinguished the candle on Pentecost. Post-2007, some churches have moved toward the more traditional, extraordinary ritual. This may explain some confusion over liturgical practices surrounding the Paschal candle, but both are allowed within the singular Roman rite.