SHA256 is a one-way cryptographic hash function which has several purposes in computer programs. It is part of the SHA-2 family of functions developed by the NSA and published first in 2001. It takes an arbitrary input string of any length and generates a 256 bit length output string, which is usually represented as a 64 character hexadecimal number such as 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824, which happens to be the "SHA256 hash" of the word "hello".
In modern times, SHA256 is still considered very secure and can be used in sensitive applications such as password hashing or financial security (such as Bitcoin). At the cost of slightly more processing power, one could even use SHA384 or SHA512 which generate similar, but longer, hashes. For more information, see this wikipedia article on SHA-2.