The intended purpose of pamphlets like Common Sense and The Crisis #1 were to build public opinion for something that was very controversial: American Independence from the British Crown. It is important to remember that many people living in the American colonies considered themselves to be, first and foremost, British.
It was considered treasonous by many in the Colonies to declare the need for independence. There needed to be a publicity campaign to build American support for revolution, and these pamphlets helped to create that debate and convince people of something that was once considered unheard of.
Eliza tried humming it before she tried to sing the song.
It is by listening and evaluating the speaker's questions and responses. When the speaker asks a question, he is surely making a point to the audience through his responses. By that kind of communication, the speaker should have given his purpose to the audiences.
It means most important. For example, a priority for you would be to get good grades. It's currently the most important thing for you right now.