A highly composite number has more divisors than every positive integer below it. Where a prime is as indivisible as a number can be, a highly composite number is the opposite extreme — maximally divisible — which is why they're nicknamed anti-primes. The first few are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040.
Srinivasa Ramanujan studied them systematically in a celebrated 1915 paper, deriving deep facts about the shape of their prime factorizations (the exponents never increase as the primes grow, and the largest prime factor is usually small). Their divisibility is why they show up everywhere humans want a number that splits evenly many ways: 12 hours, 24 hours, 60 minutes, 360 degrees, and the 5,040 that Plato proposed as the ideal city's population are all highly composite.
NumberWiki identifies them from a divisor-count sieve up to one million.