It's basically a type of battle where all the type weaknesses/resistances are reversed. For example, usually Water would be super effective against Fire, but in Inverse Battles it's vice versa - Fire is super effective against Water. A whole type chart is in the above link.
That's all there really is to Inverse Battles. Everything else is generally the same. Note, moves with types that would normally do 0x damage is turned into 2x instead of 4x in Inverse Battles.
Hope I helped. :)
Source: Above Link and Experience