"Countability" is a mathematical concept relating to the popular concept of "size" of a collection of any elements.  What it means is best illustrated in sort of an operational way.

If we have a group of objects, they are said to be "countable" if we can match the objects, one by one, with the numbers with which we customarily count, i.e. 1, 2, 3, 4, etc.  These are called the natural numbers or the non-zero, positive integers. 

Although countable there are some mathematical objects which are infinite.  What that means in popular language is that there is no last one. The counting numbers themselves are a countable, infinite set.  Many interesting articles can be found on line using a search engine and the terms "mathematics" and "countability."

You may find a good search engine, which is an alternative to Google and Yahoo at: http://www.prolifesearch.com/  (Notice that this site appears to use the google search engine.  When I challenged them on this they gave me a technical explanation I do not understand.  But I have taken them at their word, for the time being.)

Another useful search tool is available at http://www.kartoo.com/en/kartoo.html