After the singing of the Glory to God, the altar server brings the Missal to the presider and, after he opens it, he says "Let us pray." Ideally, he leaves a moment of silence here, although in practice, we all have been at Masses where there is no more than a split second. Here is why silence is so necessary: this invitation to pray is not so much about the words he will speak in the Collect (formerly the Opening Prayer), as it is about what each person present is being asked to do at this point.
The new General Instruction of the Roman Missal says this:
Next the Priest calls upon the people to pray and everybody, together with the Priest, observes a brief silence so that they may become aware of being in God’s presence and may call to mind their intentions. Then the Priest pronounces the prayer usually called the “Collect” and through which the character of the celebration finds expression. (54)
The practice by many priests of leaving little or no silence here says to me that either they were not properly formed about the purpose of the silence, or they have little regard for the participation of the people. (One of the small delights for me of celebrating Mass with my new local Bishop, R. Daniel Conlon, has been that he leaves significant and noticeable silences at all of the points in the Mass where the rubrics direct the priest to do so.)
So, what is the catechetical implication for this? Adults and children need to know they have the right to come to Mass bringing their own intentions for the celebration to lay before God at the altar. Besides the published intention of the Mass that day, this prayer of the people, offered through Christ to the Father, carries their own individual needs and intentions for the needs of their families and friends to the very throne of God. So, part of the preparation of every person coming to a Mass should be a moment to consider what they need to offer up to God that day in prayer.