The first part of your question has been answered before on this site. I'll confine my answer to the second part. Please follow the second link to find a very good answer for the first part of the question.
Puritan government was theocratic. That means that it was ruled on the basis of religious belief. The Puritans believed that God would punish their society if it allowed wrong actions and/or beliefs to exist within it.
Therefore, only Puritan church members were allowed to vote. The leaders of the church were also the leaders of the government (this is within towns, not within a whole colony). They enforced religiously based laws and they used tax money to pay for Church buildings, minister salaries, etc.
The Puritans can be described in the following way:
1. They were mostly Calvinist. This basically means their theology was from the insight of the Protestant Reformer John Calvin.
2. Puritan theology emphasized things such as sin (total depravity of man), God's grace in salvation, and the importance of the mortification of sin.
3. They also moved to America to created a community of God that would be a light on a hill to bless the world.
4. Within this society, morality was important and immorality would be shunned both religiously and socially.
5. Adultery was seen as a serious sin and a person could easily become a social outcast.
6. Finally, in terms of government, some may have believed that the proper government should be a theocracy, but many other believed in a separation between church and state. George Whitefield would be an example.