份, 个, 本, 两: How do they function in these sentences? I've been working with Rosetta Stone for about 2 weeks now, and due to the immersion (from the start, the entire program is entirely Chinese—no English anywhere), they don't do any explaining of grammatical concepts, they just demonstrate them.

I've come across four phrases that appear to be demonstrating some grammatical concept that I don't understand.

Here they are:


  
  一辆车
  一个鸡蛋
  五本书
  五份报纸
  


So I understand these to mean


  
  a car
  an egg
  five books
  five newspapers
  


Let's take #3. 五本书. I get that 五 is 5 and 书 is book. How does 本 function here? Is it a plural marker? Is there something with number words? Because it also seems like you can say 一匹马. So is 匹 here a plural marker? If these are plural markers, why are there so many?

To distill my question down, what is the word that often comes between a number and a noun? Are these phrases actually different, but they seem similar? It almost seems like every word has its own plural marker (if that's what these are). Are there more that I don't know about?
As others have mentioned, these are measure words (also known as classifiers*). To give a basis of comparison, in English measure words generally occur for uncountable nouns. For instance, because "bread" is uncountable, you cannot say "*three breads"; you must say "three loaves of bread" or "three slices of bread" ("loaves" and "slices" are the measure words in these examples).

In Chinese, all nouns are considered uncountable, and thus must have a measure word. Many nouns have a particular measure word associated with them (e.g., vehicles are typically measured by 辆; objects with a stick-like shape by 支; objects with handles by 把, etc.), and you simply have to remember which measure word is typically used with which noun. In many cases, the generic measure word 个 is acceptable.

Some measure words themselves can be treated as nouns, in which case they can have their own measure word too when you use them this way. For instance, "three bowls of rice" would be 三碗饭, but when you use 碗 as a noun, you would say 三个碗 which refers to "three bowls (of nothing in particular)". If you simply said 三碗, it would imply a measure of a noun that was already understood in context (for instance, of rice if the conversation was already about rice).

* Some make a distinction between the terms "measure word" and "classifier", but many people use them interchangeably. See the linked Wiki articles for more details.