Max was a synthetic robot, or synthoid, used by the Landoran Alliance in their war against the Averon Union.
It started its existence as Synthonic Mobile Infantry Unit, Trooper Class: serial number 36025D. When it was sent to Tarracos, its designation was changed to Mobile Armed Auxiliary to fit the local command structure. The unit was damaged on the fifth planet of Tarracos, causing it to create alternate neural paths in its brain. This led to it becoming the first self-aware synthoid. Sarah Jane Smith met the synthoid not long after it was damaged. She came up with the more succinct and human sounding name of Max for it.
After Sarah was reunited with the Fourth Doctor and Harry Sullivan, Max helped the Doctor find out the truth about the war. They pretended to be Tralsammavarians, with Max being the Mogul, and tried buying weapons from Kambril.
The fact that the war was a sham was finally revealed, and Kambril arrested. Deepcity was going to be shut down, but Max revealed he was going to take it over and create an army of self-aware weapons to keep the peace from then on. The Time Lord Brastall revealed that Max's "descendants" would help in the ultimate defeat of the Daleks in the future. (PROSE: A Device of Death)