What is a "term-vector algorithm"?

Question

Google states that a "term-vector algorithm" can be used to determine popular keywords. I have studied http://en.wikipedia.org/wiki/Vector_space_model, but cant understand the term "term-vector algorithm".

Please explain it in a brief summary, very simple language, as if the reader is a child.

I believe "vector" refers to the mathematics definition, a quantity having direction as well as magnitude. How is it that keywords have a quantity moving in a direction?

http://en.wikipedia.org/wiki/Vector_space_model states "Each dimension corresponds to a separate term." I thought dimension relates to cardinality, is that correct?

From the book Hadoop In Practice, by Alex Holmes, page 12.

Answer 1

It means that each word forms a separate dimension:

Example: (shamelessly taken from here)

For a model containing only three words you would get:

dict = { dog, cat, lion }

Document 1
“cat cat” → (0,2,0) 

Document 2
“cat cat cat” → (0,3,0)

Document 3
“lion cat” → (0,1,1)

Document 4 
“cat lion” → (0,1,1)