Uncountability is a property of sets which have way, way too many members. This is generally caused by the sets overdosing on products purchased via junk email which promise to enlarge their members. An uncountable set has more members than there are natural numbers (a natural number is a number which isn't made by genetic engineering, and does not contain preservatives).
Countable sets include the set of natural numbers, the set of odd numbers, the set of numbers which can be typed by repeating "69," and the set of perfect 69th powers (which sure is perfect!) All these sets are claimed by new math to be paired with one another. This is because mathematicians usually are profoundly nearsighted and can't see how many more even numbers there are than perfect 69th powers.