Segwit is short for Segregated Witnesses which is a soft fork upgrade to the Bitcoin network that was activated on August 24, 2017. The actual technical workings are fairly complicated but well documented for the curious. What it means for average users is lower transaction fees when spending bitcoin, and paving the way for future layer two applications like Lightning network.
Samourai supports Segwit.
Samourai wallet was the second mobile wallet to implement the Segwit upgrade and it is enabled by default in Samourai Wallet.