It's a feature originally developed for Bitcoin:

https://bitcoincore.org/en/2016/01/26/segwit-benefits/

Litecoin is based on Bitcoin Core's codebase and therefore inherited it as well. Due to various reasons it's activating on Litecoin before Bitcoin.

A somewhat controversial protocol upgrade developed for bitcoin. On the bitcoin network it has not reached the necessary support yet. Most bitcoiners view its activation on litecoin as a large scale beta test.

It's a protocol change that moves signature scripts out of the transaction itself, such that they are not included when calculating the hash/transaction ID of a transaction (a signature script contains both a signature plus additional data needed to fulfill a particular output script; only the additional data can the modified while keeping the signature valid). This is important because the signature script itself is unsigned data (a signature can't sign itself), which means that it's possible to change the signature script of a transaction, thus changing the transaction ID, and invalidating all transactions that pointed to the original transaction. This is colloquially referred to as "transaction malleability".