I'll give you land and in return, you have to fight for me.
Absolute Monarchy
I'm the queen of this kingdom and I have absolute power over everyone.
Republic
The people voted for me as their president but I don't have full control like a ruler.
Feudalism was a system where the Kings were on top then followed by the Nobles, Knights, and Vassals. Without one of the 4 ranks, the entire system would fall apart because each one depended on the other to fulfill their role. In feudalism, people were given land and protection and in return, they would have to work and fight for people of a higher rank. An example of a feudalism system government was Mediveal Europe.
Theocracy
I'm a priest and a believer of God and i'm in I rule the government.
Absolute Monarchy is a system where the king or queen has all of the power over everyone. In absolute monarchies, the succession of power is typically hereditary, with the throne passing among members of a ruling family. So in an absolute monarchy, someone from a different family can't be in power. The only absolute monarchy existing is in Saudi Arabia and its ruler is Salman bin Abdulaziz al Saud.
Direct Democracy
We the people make all of the decisions and we vote on them. 
A republic is a system where the people vote for their leader and everyone in their government. And that leader doesn't have full control of the people, just the government, and makes the final decisions. Also, supreme power is held "by the people" and a republic is for the people. An example of a republic is Mexico.
Aristocracy
Our family is the highest class in the kingdom.
Theocracy is a system of government where priests rule in the name of God. A religious priest runs the government in a religious way. They can support God or another god and its not for a specific religion, its for any religion they chose. An example of this is Iran.
Direct Democracy is a system of government where the people vote on all of the decisions. Even if a budget or a law needs to be passed, the people still have to vote on it. But, large governments rarely use direct democracy because the people would think differently. Switzerland is one of the only countries who use Direct Democracy.
Aristocracy is a system of government where a wealthy family or the (highest class) had the power. It's usually a small, privileged class and heredity was not the answer unless if their ancestors were the best. If your ancestors were already "the upper class", then they had a higher chance of ruling over. An example of the is Medieval England.