A priest in the LDS Church is a priesthood office to which young men are ordained at the age of 16, or adults who are still progressing to higher priesthood offices. Most men in the church will be ordained priests after ecclesiastical interviews with their leaders and through demonstrating faithful living. From D&C 20:
60 Every elder, priest, teacher, or deacon is to be ordained according to the gifts and callings of God unto him; and he is to be ordained by the power of the Holy Ghost, which is in the one who ordains him.
A priest has responsibilities in the church to administer the sacrament, see that meetings are held regularly and in accordance with the Spirit, and to help take care of physical needs of the congregation:
46 The priest’s duty is to preach, teach, expound, exhort, and
baptize, and administer the sacrament,
47 And visit the house of each member, and exhort them to pray vocally
and in secret and attend to all family duties.
48 And he may also ordain other priests, teachers, and deacons.
49 And he is to take the lead of meetings when there is no elder
present;
50 But when there is an elder present, he is only to preach, teach,
expound, exhort, and baptize,
51 And visit the house of each member, exhorting them to pray vocally
and in secret and attend to all family duties.
52 In all these duties the priest is to assist the elder if occasion
requires.
Oh, and priests are also typically educated in seminary, in areas where it is available. In most parts of the world, members who are high school age go to seminary class before or during school. Its a four year program of scripture and doctrine study. These classes are also for the young women.
Unlike other Christian denominations, a priest does not necessarily give a sermon on Sundays. Speakers are chosen by the local priesthood leaders and can be nearly anyone in the ward (local congregation).
I'm mobile now but if required I can cite some scriptures.