I desire then that in every place the men should pray, lifting up holy hands without anger or argument (1 Timothy 2:8 NRSV).
Someone recently asked me about the propriety of people in the congregation extending their hands at the Our Father, in a gesture similar to that which is prescribed for the priest at certain parts of the Mass (e.g., the three orations, the Eucharistic Prayer, the Our Father and the prayers that immediately follow it). Apparently there has been some occasional chatter on various internet sites and blogs about this topic, traditionally known as the orans position, regarding whether or not it is appropriate for laypeople to extend their hands in this manner at Mass, specifically at the Our Father.
Now I am not at all an expert on the history and liturgical use of the orans position. And I am sure there are others who are experts. I have, however, always assumed (reasonably, I believe) that the rubrics directing the celebrant to extend his hands in this fashion at certain parts of the Mass represent a formalized, somewhat stylized version of an ancient, widely used (and originally probably more expansive) prayer gesture (cf. Psalms 28:2, 63:4; 134:2; and 141:2). Both the Old Testament and the New (cf. 1 Timothy 2:8, above) imply that this gesture was widely used in popular prayer.
At Mass, the celebrant is directed to extend his hands in the ritualized version of the orans position at the various prayers mentioned above, as well as when he greets the people with The Lord be with you (except at the Gospel, when he is explicitly directed to keep his hands joined). If there are concelebrants, only the principal celebrant does so - except at the anamnesis after the Consecration which all the concelebrants recite together, at the Intercessions in the Eucharistic Prayer when the concelebrant who is speaking does so alone, and at the Lord's Prayer when all the concelebrants are again invited to extend their hands while reciting the prayer (but only for the Lord's Prayer, not for what follows). The posture is, however, nowhere prescribed for the deacon.
As far as I am aware, while congregational postures (standing, kneeling, sitting) are specifically prescribed, no directions are given at all about the people's hands. There are inherited cultural traditions, of course, that recommend what to do with one's hands (e.g., holding them together or folded), but that is about it.
If I recall correctly, back in the 1990s, the US Bishops discussed a recommendation that the people extend their hands at the Our Father. This was presumably an attempt to counter the unfortunate custom that had arisen in many places since the 1960s of people holding hands during the Our Father, a custom which inevitably horizontalizes the focus of the prayer. It was, I think, thus a commendable attempt to replace a modern, untraditional, and unliturgical practice of hand-holding with something ancient, traditional, and liturgical. In fact, however, the proposal was attached to the problematic ICEL translation of the 2nd edition of the Missal. Since that translation was rejected by Rome and never implemented, neither was the orans recommendation ever formally implemented.
But it does seem to have caught on - at least in some places. And, since there are no specific rules prescribing what people should do with their hands, there would seem to be no specific prohibition either. If nothing else, certainly it is more appropriate and more meaningful - certainly more ancient, traditional, and liturgical - than holding hands!
But, remembering what Paul wrote to Timothy, whatever is done let it be without anger or argument!