There are two main types of data that you might encounter. The first is discrete data, which is a count of whole events, objects or persons. For example, the number of people with a certain illness is a discrete quantity, ie, countable.
The other type of data is continuous data, which is the measure of a quantity such as length, volume, or time, which can occur at any value. For example, the concentration of glucose in the blood is a continuous quantity. Even if the instrument you are using rounds off values to whole numbers, these quantities are still continuous; ie, not countable.