These ministers distribute the Lord Jesus in the Eucharist at Mass as assistants to the priest when other ordained ministers are not available.
In addition to serving at Mass, some Ministers may bring the Eucharist to parishioners who are sick or housebound.
The following extract from Chapter 7 of the Holy See Instruction Redemptionis Sacramentum gives some background information.
The Extraordinary Minister of Holy Communion
[154.] As has already been recalled, “the only minister who can confect the Sacrament of the Eucharist in persona Christi is a validly ordained Priest”. Hence the name “minister of the Eucharist” belongs properly to the Priest alone. Moreover, also by reason of their sacred Ordination, the ordinary ministers of Holy Communion are the Bishop, the Priest and the Deacon, to whom it belongs therefore to administer Holy Communion to the lay members of Christ’s faithful during the celebration of Mass. In this way their ministerial office in the Church is fully and accurately brought to light, and the sign value of the Sacrament is made complete.
[155.] In addition to the ordinary ministers there is the formally instituted acolyte, who by virtue of his institution is an extraordinary minister of Holy Communion even outside the celebration of Mass. If, moreover, reasons of real necessity prompt it, another lay member of Christ’s faithful may also be delegated by the diocesan Bishop, in accordance with the norm of law, for one occasion or for a specified time, and an appropriate formula of blessing may be used for the occasion. This act of appointment, however, does not necessarily take a liturgical form, nor, if it does take a liturgical form, should it resemble sacred Ordination in any way. Finally, in special cases of an unforeseen nature, permission can be given for a single occasion by the Priest who presides at the celebration of the Eucharist.
[156.] This function is to be understood strictly according to the name by which it is known, that is to say, that of extraordinary minister of Holy Communion, and not “special minister of Holy Communion” nor “extraordinary minister of the Eucharist” nor “special minister of the Eucharist”, by which names the meaning of this function is unnecessarily and improperly broadened.
[157.] If there is usually present a sufficient number of sacred ministers for the distribution of Holy Communion, extraordinary ministers of Holy Communion may not be appointed. Indeed, in such circumstances, those who may have already been appointed to this ministry should not exercise it. The practice of those Priests is reprobated who, even though present at the celebration, abstain from distributing Communion and hand this function over to laypersons.
[158.] Indeed, the extraordinary minister of Holy Communion may administer Communion only when the Priest and Deacon are lacking, when the Priest is prevented by weakness or advanced age or some other genuine reason, or when the number of faithful coming to Communion is so great that the very celebration of Mass would be unduly prolonged. This, however, is to be understood in such a way that a brief prolongation, considering the circumstances and culture of the place, is not at all a sufficient reason.