Formal politics is politics as defined by law. Essentially, everyone follows the rules. One man, one vote, everyone follows the rule of law, people can petition their government for wrongs and have them heard, and so on.
Informal politics isn’t really defined, but it is when there are other forms of communication channels used that aren’t supposed to be there. In the United Nations, this takes the form of backdoor channels and is considered a good thing. (For example, two blood enemies talk together secretly to reduce tensions or lay the groundwork for an agreement when it would be political suicide for their citizens to know negotiations are going on. Example: Egypt and Israel peace agreement. Lots of informal negotiations preceded the actual peace talks and agreements.)
In Western countries, informal politics serves both to help and hurt the legitimacy of the political process. For example, Senator Daschle is not