Segregated Witness (SegWit):

What it is and what it does

SegWit is a concept that was created by Dr. Pieter Wuille, a developer for the Bitcoin Foundation, to overcome the limitation of the number of transactions that can be included in a single Bitcoin block. 

Segregated witness is a method by which the digital signatures for individual transactions are removed when blocks are created (and before they are added to the blockchain).  By removing the signatures, more space is available in the block to hold transactions, thereby increasing the number of transactions in a block.  The signatures are moved to the end of the transaction into what is ostensibly a completely separate area that does not use space in the actual transaction block.

Digital signatures account for approximately 65% of the space taken for a transaction.  By removing this data, the number of transactions can be increased by as much as 180%.  In addition, because the signature data is segregated from the transaction, anyone who intercepts the transaction with the intent of changing the transaction has no way to digitally sign it and resubmit it, thereby increasing the security of the blockchain.

Currently, several coins have implemented SegWit, including Litecoin, Bitcoin,and others.  While SegWit has been implemented in Bitcoin, in order to be activated 95% of the community must switch to the new Bitcoin Core client for at least two weeks.  Currently, the code is there it just remains inactivated.  SegWit is fully activated on Litecoin.  SegWit was implemented on both Litecoin and Bitcoin as a soft fork, meaning that the new addresses and blocks are fully compatible with older versions.

The network can tell the difference between a SegWit and a legacy transaction based on the source and destination addresses.  In Litecoin, a legacy address begins with an "L".  Originally, SegWit addresses in Litecoin began with a "3" address.  However, it was determined that the Bitcoin address space may also overlap the Litecoin SegWit "3" space.  To avoid any confusion, Litecoin changed the SegWit preface to an "M".

Anyone can convert between Litecoin's older "3" and newer "M" segregated witness addresses using the converter that was created by developers at the Litecoin Foundation.  The converter will also convert legacy addresses to SegWit "M" addresses.

An excellent resource for additional information can be found on the blog for the Trevor hardware wallet, while a far more technical description (with some really good political background) can be found on the Wikipedia page.