Taking the second power of a number is called taking its square.
Two is the base of the binary system, used in computers.
2 is a Mersenne exponent, producing the prime 3. The next exponent is 3.
2 is the second highly composite number, being the first with 2 or more factors. The next one is 4. It is the only prime highly composite number.
Testing for divisibility by 2 is as simple as checking if the last digit is 0, 2, 4, 6, or 8. If it is, the number is divisible by 2. For instance, 234748 ends in 8 and is a multiple of 2.