I'll try to improve on the prior answer since one shouldn't use the word you're trying to define in its own definition.
These are different kinds of history; most professional historians specialize in one or another of these approaches, since nobody can do everything.
Politics is the way that power is exercised in a given society. Therefore, political history is the study of how power relations operate in a society over time; how do people get power, what kinds of power do they have, how is power distributed or balanced (all in a single monarch or dictator, or divided among different people or institutions?), etc.
Social history is best understood as how societies are organized into different groups or categories of people, and how these groups relate to each other. What makes a person upper, middle, or lower-class? What are the differences between the lives of men and women? Of the young and the old? How are ethnic or racial differences constructed and managed? Is there a noble class, or slavery? Things like that.
Economics is the study of wealth, so economic history is, like political history, the study of wealth in a given society. How is it produced? How is it distributed? How is wealth consumed? For instance, how does agriculture, or industry, or trade operate?
Cultural history is a very broad and malleable kind of history. It is best thought of as the study of "mentalities" -- of the way that people think and feel about things, or of the attitudes that they have toward things, or of how they express themselves. For instance, if you study the ethics and values of a given society, that would fall under cultural history. So do studies of religion, or of the arts and media, or of general attitudes in the society.
Notice that these categories can easily blur into each other and overlap. For instance, supposing you are studying women in a given society and period -- say WWI Germany. If you look at the numbers of women, their life expectancies, marriage rates and average age at marriage, women's legal rights and protections, average number of pregnancies per woman, representation of women in the work force, careers they did and didn't pursue, etc., you're doing social history. But almost inevitably, in studying this stuff, you're going to start running into attitudes towards women; chauvinism and sexism, feminism, images of women as inferior to or dependent on men (rationalized in various ways), defenses of women as capable or virtuous, images presenting "ideal" women and notions of beauty, etc. All of that kind of thing is cultural history.