Well, so the big hidden question here is "what comprises an LDS sunday service?". A related question covers some of this, so I'll just summarize. In your average "Sacrament meeting", you'll typically have:
- 1 who presides at the meeting
- 1 who conducts the meeting (may be the same as the one presiding)
- 1 who leads the music
- 1 who plays the piano/organ
- 2+ who bless the Sacrament (Eucharist)
- several who pass the Sacrament to the congregation
- 2 who say the opening and closing prayers
- several who give short talks or sermons
Of these, the only thing women may not do is preside at the meeting, bless the Sacrament, or pass the Sacrament. Those are duties of people who hold the Priesthood, and only men hold the Priesthood.
It would be very unusual to see a woman conduct the meeting, since that is usually done by the presiding person or one of his counselors. However, there are some meetings of the Church where women conduct the meetings (for example, the General Relief Society Meeting). There are also meetings where women preside (again, most meetings of the Relief Society), but that does not happen in a Sacrament meeting.
The LDS website gives a very succinct answer to this:
In weekly worship services and classes, women preach sermons, offer prayers in behalf of the congregation, and teach adults and children. They may also serve as missionaries and as presidents of the Relief Society, Young Women, and Primary organizations. Women participate in councils that oversee congregational activities throughout the world. They also perform a vital work in nurturing and teaching in the home.
The page linked to above contains many links to more information, but in short, women hold an important place and serve as teachers and role models, and are in authority in certain positions.
There are positions they cannot hold: most significantly, the priesthood. From the BYU's wiki:
Particularly, they are not allowed to hold the position of Priesthood, which limits them from holding other positions within the Church that are only available to those in the Priesthood.Women and men, although equal in status, fulfill some separate and different roles in the work of the Church. To men is given the responsibility of holding the priesthood, with many prescribed duties. The role for women is less precisely defined, though no less real. According to Neal A. Maxwell of the Quorum of the Twelve: We know so little about the reasons for the division of duties between womanhood and manhood as well as between motherhood and priesthood. These were divinely determined in another time and another place. We are accustomed to focusing on the men of God because theirs is the priesthood and leadership line. But paralleling that authority line is a stream of righteous influence reflecting the remarkable women of God who have existed in all ages and dispensations, including our own [Maxwell, p. 94].
The duties of the Priesthood are covered here, which gives some insight, but not specifics of exactly what women are, and are not allowed to do.