Scrypt is the mining algorithm used to mine Litecoin (LTC). Scrypt was invented by Colin Percival in 2009 to be used as a memory hard cryptographic hash function. A “memory hard” function uses large amounts of memory in order to compute the end result. This hinders the development of custom hardware that can be used to brute force the function, commonly known as ASICs.
Scrypt was first used in Tenebrix in 2011, which Charlie Lee cloned to create Fairbrix. Both projects failed to gain any traction mostly due to their premine. Lee then created Litecoin as a response and the project has been a constant presence in the cryptocurrency scene since.
Along with Litecoin, Scrypt is also used to mine Dogecoin (merge mined with Litecoin), and Digibyte (in Digibyte Scrypt is one algo in a multi-algo POW system).
Although the initial goal of Scrypt was to hinder the development of ASICs, ASIC mining is now the norm and has been since around 2014. Currently, Bitmain’s L3 series is the most prevalent ASIC and much of Scrypt mining happens professionally alongside Bitcoin mining operations.