There are several key passages in Sacrosanctum Concilium from which we discover the Council’s meaning in this seminal phrase. The most succinct may be at SC 48 which tells us what both what this participation is not as well as what it is:
And so the church devotes careful efforts to prevent Christian believers from attending this mystery of faith as though they were outsiders or silent onlookers: rather, having a good understanding of this mystery, through the ritual and the prayers, they should share in the worshipping event, aware of what is happening and devoutly involved. They should be formed by God’s word, and refreshed at the table of the Lord’s body; they should give thanks to God; they should learn to offer themselves as they offer the immaculate victim – not just through the hands of the priest, but also they themselves making the offering together with him; and, as each day goes by, they should be led towards their final goal of unity with God and among themselves through the mediation of Christ, so that finally God may be all in all.