What is this is the type of government where individual citizens can participate freely in there government through voting and have many personal freedoms

The answer to this question is democracy. Democracy is a form of government where the power is exerted by the citizens - directly or through their representatives. It is the opposite of other forms of government such as autocracy (government of one person) or oligarchy (government of a few). In a democratic society all members have the same rights.

That kind of government is called Democracy.

Democracy (from the late Latin democratĭa, and this from the Greek δημοκρατία dēmokratía) is a form of social organization that attributes the ownership of power to the whole of citizenship. Strictly speaking, democracy is a form of State organization in which collective decisions are adopted by the people through mechanisms of direct or indirect participation that confer legitimacy on their representatives. In a broad sense, democracy is a form of social coexistence in which members are free and equal and social relations are established according to contractual mechanisms.