I tried the wiki, but couldn't find any information on this cool-looking walking (hydron?) canon. What is the name of this and what does it do?
It's a Japanese Seige weapon which was originally developed by the Japanese Liberation Front, first seen in the JLF's Hotel Hijacking which saw Euphie held hostage and the rise of the Black Knights. it was later used by the Black Knights duing the Assault on Tokyo Settlement in the Black Rebellion.
As it's translated name suggests, it's a lighting cannon, more precisely it's an Electromagnetic Cannon using the 4 Knightmares to move it around and to stabilize when it's being fired, in the anime we only see 2 crew members so there isn't one in each Knightmare. only Suzaku and the Lancelot is shown to be able to destroy it.