A "countable set" in that it has the same cardinality as the countable numbers (1, 2, 3, ...). For instance, the primes are countably infinite; you can map the set of primes onto the countable numbers (the first prime number is 2, the second is 3, the third is 5, ...). The term comes from Georg Cantor's work in the late 19th century.
Notably, while the set of rational numbers is countable, the reals (including transcendental numbers such as e and pi) are not; there's a fairly simply proof using diagonalization that you can Google, although that's not how Cantor originally demonstrated it.
Notably, while the set of rational numbers is countable, the reals (including transcendental numbers such as e and pi) are not; there's a fairly simply proof using diagonalization that you can Google, although that's not how Cantor originally demonstrated it.