Mormonism lacks a trained clergy; never had it, never will. So where did the Mormon tradition of a lay ministry start and what did it use for its initial format or example? Much of it was drawn from Methodism. Both Joseph Smith, Jr., and John Taylor, for example, served as Methodist Exhorters as teenagers (see JS-H 1:7-8 and Anderson, Inside the Mind of Joseph Smith, Signature Books, 1999, p. 39 for Joseph; this short bio for John Taylor). What exactly is a Methodist Exhorter and what did they do?
The modern office that discharges that role in the Methodist Church is called Lay Speaker, and they have their own Lay Speaking Ministries site. A short history of the Exhorter/Lay Speaker office is provided. They didn't preach sermons or interpret scriptures publicly--they couldn't. They had no training. They would just have spread screwy interpretations leading to confusion and serving to discredit the church. So they just "exhorted" by urging folks to pray and repent, offering encouragement, and admonishing listeners to act. Sound familiar?
Here's a quote for what early Methodist Exhorters in England did: "They did not 'preach' in the usual sense of that term, but held meetings for prayer, and addressed the people on the subject of religion, giving them requisite encouragement and admonition and calling 'them that were without' to repentance" (the article is quoting Simon, 1923).
Here's how it worked in America: "Early exhorters in the American church were used to 'exhort' the people to follow God's Word and to live exemplary lives. They would often 'exhort' the people to action after the appointed clergy had 'preached' the sermon" (from the article). The modern Methodist regulations noted in the article require local church lay speakers to take a basic course and certified lay speakers to take the basic plus one of several advanced courses. These aren't "trained ministers." In the Methodist Church you need training just to be the lowest of lay speakers. Training improves performance; it is a form of quality control for the provision of services. Quality preaching matters to Methodists, it seems. I'm jealous.
It's pretty clear that early Mormon leaders, Joseph included, designed Mormon services around their exhorting experience. They had no ordained clergy to preach proper sermons from a text. No liturgy, no clergy, just hymns, a simple eucharist ordinance, and plenty of praying and exhorting. That still defines Mormon services to this day. General Conference is just exhorting writ large with a better choir.
If this helps you understand the origin and structure of the Mormon approach to Sunday services, it might also help you understand what goes on each Sunday in church. Getting a little tired of being exhorted at for 60 minutes every Sunday? Have you ever found yourself (gasp!) thinking that maybe having a trained minister to preach a proper sermon wouldn't be so bad? Think how things would change if every Mormon sacrament meeting speaker had to take a 10-hour basic lay speaker course before inflicting themselves on the congregation. I mean it's only the gospel of Jesus Christ we claim to be preaching on Sunday--you would think leaders would take it more seriously. At least as seriously as Methodists do.