Tithing, quite simply, is giving a portion of the gifts which God has given us back to Him in thanksgiving for them. These gifts usually fall under the categories of Time, Talent, and Treasure.
We give of our time and talents in service to the needs of Christ and the Church by participating in the ministry of the Church, ministries which can be as diverse as teaching children or adults on the way to conversion, building and grounds maintenance, or helping the less fortunate, especially the poor, the sick, and the grieving.
We also give of our treasure in the same service as our time and talent, but our treasure is given as financial support of the ministry of the Church. Christians are called to "give whatever [they] can afford." (1 Corinthians 16:2) Thus, we are not bound by the ten percent of the Old Covenant.