In the "Catechism of the Catholic Church" Articles #1030 to #1032 explain the Church's teaching on Purgatory. If you do not have a copy of the Catechism you can find it online. http://www.scborromeo.org/ccc/ccc_toc.htm (scroll down to Article 12)
In a recent parish bulletin one of our pastors made a comparison between the rescue of the Chilean miners and the souls in Purgatory. "Their long awaited moment of freedom came about through a cooperative effort (of many people) all under the providential influence of God's grace." We can pray for our deceased brothers and sisters to speed them along their way to eternal rest.