March 3, 2015
The postures of the priest, deacon, and congregation during various portions of the Mass are contained in either the Roman Missal or the General Instruction on the Roman Missal (GIRM). The current GIRM contains some explicit rules about the postures of the congregation during portions of the Mass, such as making the sign of the cross during the introductory rite, standing at the Gospel and sitting during the homily.
There are two separate issues here, so let me address the holding of hands first. Holding hands is not a liturgical action and is rarely called for during the Mass. The only place in any liturgical book where the faithful are instructed to hold hands is in the Liturgy of the Sacrament of Matrimony where the priest or deacon receives the couple’s consent and states
“Since it is your intention to enter into marriage, join your right hands, and declare your consent before God and his Church.” My recommendation with this is, if it not an instructed action, don’t do it. The hands of the faithful should be folded in prayer during the Our Father.
The second issue is the outstretched hands. This position to which you refer is known as the orans position (from the Latin word for pray). This position during Mass is symbolic of leading in prayer. It is called for to the priest alone during the Our Father. Similarly, there are instructions for the priest to assume the orans position during the Eucharistic Prayer (consecration). It is a position that is reserved for the priest as he leads prayer.
When in doubt as to what to do with your hands during Mass, you cannot go wrong with keeping them respectfully folded.