I 夷 is a derogatory term for 'foreigner' or 'barbarian'
Combined the phrase literally means 'expel-the-foreigners'
Shishi 志士 means 'patriot', though in the Gintama context 'rebel' may be more appropriate
There are actually a number of different factions within the Jouishishi rebellion, some more extremist than others. Katsura's faction grew moderate as the anime progressed, from the the initial opening scene in Episode 5 where Katsura used terrorist-like tactics like time bombs liberally, to the Benizakura Chapter Episode 61 where he pleaded with Takasugi Shinsuke that there must be other ways of changing the world other than destroying it all. However, he was still happy to deploy bombs liberally against Shinsengumi 真選組.
Their anti-government and/or terrorist activities made them the arch nemesis of the Shinsengumi 真選組, who had made it their mission to wipe out the rebellion movement. However, the extremist factions are known to have secret dealings with the Bakufu government, for example in Episodes ?.verification/corroboration needed
