Branches
Government has 3 main arms: Legislative (to make laws and oversee policies), Executive (to provide services as designed at a high level by the legislature) and Judiciary (to take care of grievances, punish wrong-doing).
Importance
Government design determines the type and the quality of the services provided by the government. Bad governments are often a result of bad design.
Legislature
Legislatures have great power because they determine the laws/ policies; the executive and judiciary merely execute them.
Legislatures vary in the extant to which they fear the people rather than the people fearing them. The more the legislature fears the people, the better quality of life people often achieve.
Lobbying
Special interest groups (serving the interest of foreign nations, or industry segments, for example) try to influence, often very successfully, the laws and policies designed by the legislature in order to be favorable to them.
They may do these by propaganda and dialogue to honestly convince that the ideas they support are good - for not just the legislator. But, they also often resort to appealing to the self-interest rather than the legislator’s duty (except perhaps using a broader justification for the importance of staying in power) by supplying money for campaigns or by bribery.