Points usually refer to an index like the Dow Jones, S&P 500, Russell 2000 etc. Sometimes people refer to points when talking about individual stocks, but its really not proper. When refering to individual stocks it refers to dollars and cents.
It is how much a stock falls or rises. For example, let's say Dow is at $10,000, and someone says today Dow will fall 100 points. In another word he is saying it will be at $9,900 today. So yes, it's the dollar amount.
They are usually talking about points of the Dow Jones Industrial Average, see the link. However, points can also refer to how many dollars a certain stock costs.
